teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?

Explanation: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 153 ) / \ x − 153 22.50 = > x − ( 153 / 22.50 ) = 1 . = > x − 153 = 22.50 . = > x = 175.50 rs . answer : c"

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 135)), 2)

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">153 * 4</gadget>
<output>612</output>
<gadget id="calculator">126 + 135</gadget>
<output>261</output>
<gadget id="calculator">612 - 261</gadget>
<output>351</output>
<gadget id="calculator">351 / 2</gadget>
<output>351/2 = around 175.5</output>
<result>351/2 = around 175.5</result>


in what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

Explanation: "t = 50 / 36 * 18 / 5 = 5 sec answer : a"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<result>5</result>


the marks obtained by vijay and amith are in the ratio 8 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?

Explanation: 8 : 5 3 : 2 - - - - - - - 24 : 15 : 10 24 : 10 12 : 5 answer : a

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>


in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 22 overs to reach the target of 282 runs ?

Explanation: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 22 run rate needed = 250 / 22 = 11.36 answer : option b"

divide(subtract(282, multiply(10, 3.2)), 22)

<gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 22</gadget>
<output>125/11 = around 11.363636</output>
<result>125/11 = around 11.363636</result>


x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :

Explanation: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c"

divide(multiply(1, power(3, const_2)), power(9, const_2))

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1 * 9</gadget>
<output>9</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">9 / 81</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


a train running at the speed of 90 km / hr crosses a pole in 5 seconds . find the length of the train .

Explanation: "explanation : speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time = 25 * 5 = 125 meter option d"

multiply(divide(multiply(90, const_1000), const_3600), 5)

<gadget id="calculator">90 * 1_000</gadget>
<output>90_000</output>
<gadget id="calculator">90_000 / 3_600</gadget>
<output>25</output>
<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>


find the mean proportional between 64 & 81 ?

Explanation: "formula = √ a × b a = 64 and b = 81 √ 64 × 81 = 8 × 9 = 72 d"

<gadget id="calculator">64 + 81</gadget>
<output>145</output>
<gadget id="calculator">145 / 2</gadget>
<output>145/2 = around 72.5</output>
<result>145/2 = around 72.5</result>


if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?

Explanation: "given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . ."

<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<result>6</result>


what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .

Explanation: an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e

triangle_perimeter(multiply(sqrt(multiply(50, const_2)), sqrt(const_2)), sqrt(multiply(50, const_2)), sqrt(multiply(50, const_2)))

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">10 * (sqrt(2))</gadget>
<output>10*sqrt(2) = around 14.142136</output>
<gadget id="calculator">(10*sqrt(2)) + 10 + 10</gadget>
<output>10*sqrt(2) + 20 = around 34.142136</output>
<result>10*sqrt(2) + 20 = around 34.142136</result>


here 10 programmers , type 10 lines within 10 minutes then 60 lines can type within 60 minutes . how many programmers are needed ?

Explanation: 10 10 programmer 10 line 10 mins . 10 programmer 20 line 20 mins . . . . . 10 programmer 60 line 60 mins . answer : d

<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<result>60</result>


in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?

Explanation: the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d .

subtract(divide(1500, 75), divide(400, 25))

<gadget id="calculator">1_500 / 75</gadget>
<output>20</output>
<gadget id="calculator">400 / 25</gadget>
<output>16</output>
<gadget id="calculator">20 - 16</gadget>
<output>4</output>
<result>4</result>


jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 6 hours . how long would it take taimour to paint the fence alone ?

Explanation: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 6 = > 1 / 18 working alone taimour can do the job in 1 = 1 / 18 * hours = > 18 answer c"

<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>


if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 800 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 820 . what is the value of x ?

Explanation: "simple way to solve this question is to use options . from si , we know that x * y = 40,000 . now , put the value of x = 8000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 8000 + 5 % of 8000 = 8400 . 2 nd year , amount = 8400 + 5 % of 8400 = 8820 . we can see after 2 years interest = 8820 - 8000 = 820 . hence , it satisfies the question . hence a is the correct answer"

divide(power(divide(800, const_2), const_2), subtract(820, 800))

<gadget id="calculator">800 / 2</gadget>
<output>400</output>
<gadget id="calculator">400 ** 2</gadget>
<output>160_000</output>
<gadget id="calculator">820 - 800</gadget>
<output>20</output>
<gadget id="calculator">160_000 / 20</gadget>
<output>8_000</output>
<result>8_000</result>


i had 30 donuts when i left home this morning but only 9 when i came back home . what percentage of the donuts are missing ?

Explanation: 30 - 9 = 21 21 / 30 or 7 / 10 7 / 10 = 70 / 100 = 70 % answer is a

<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<result>70</result>


a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?

Explanation: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e ."

add(divide(circumface(10), const_2), multiply(const_2, 10))

<gadget id="calculator">2 * pi * 10</gadget>
<output>20*pi = around 62.831853</output>
<gadget id="calculator">(20*pi) / 2</gadget>
<output>10*pi = around 31.415927</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">(10*pi) + 20</gadget>
<output>20 + 10*pi = around 51.415927</output>
<result>20 + 10*pi = around 51.415927</result>


find the average of the first 19 natural numbers ?

Explanation: average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c

divide(multiply(divide(add(19, const_1), const_2), 19), 19)

<gadget id="calculator">19 + 1</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 19</gadget>
<output>190</output>
<gadget id="calculator">190 / 19</gadget>
<output>10</output>
<result>10</result>


if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?

Explanation: "assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice ."

<gadget id="calculator">18 / 9</gadget>
<output>2</output>
<result>2</result>


if n = 16 × 10 ^ ( - p ) and − 4 < p < 4 , how many different integer values of p will make n a perfect square ?

Explanation: i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100

<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<result>3</result>


in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is

Explanation: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c"

<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 10</gadget>
<output>30</output>
<gadget id="calculator">30 + 9</gadget>
<output>39</output>
<result>39</result>


on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

Explanation: per quarter , interest = 2.5 % so for a year , interest = 10 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 10 % answer = 10.5 % = answer : e

<gadget id="calculator">2.5 * 4</gadget>
<output>10</output>
<result>10</result>


two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

Explanation: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 15 ] m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = m / sec = 20 m / sec . ∴ required time = ( 120 + 120 ) / 20 secc = 12 sec . answer a"

<gadget id="calculator">120 + 120</gadget>
<output>240</output>
<gadget id="calculator">120 / 15</gadget>
<output>8</output>
<gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">240 / 20</gadget>
<output>12</output>
<result>12</result>


in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?

Explanation: "( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d"

divide(divide(subtract(96, 82), subtract(96, 68)), subtract(const_1, divide(subtract(96, 82), subtract(96, 68))))

<gadget id="calculator">96 - 82</gadget>
<output>14</output>
<gadget id="calculator">96 - 68</gadget>
<output>28</output>
<gadget id="calculator">14 / 28</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / (1/2)</gadget>
<output>1</output>
<result>1</result>


an article with cost price of 240 is sold at 20 % profit . what is the selling price ?

Explanation: "sp = 1.20 * 240 = 288 answer : a"

add(240, multiply(240, divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">240 * (1/5)</gadget>
<output>48</output>
<gadget id="calculator">240 + 48</gadget>
<output>288</output>
<result>288</result>


a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability r that the first ball picked up is odd numbered ?

Explanation: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability r is 2 / 3 . d"

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 460 – 320 ) / 320 ] x 100 ≈ 44 % . the answer is c ."

multiply(divide(subtract(460, 320), 320), const_100)

<gadget id="calculator">460 - 320</gadget>
<output>140</output>
<gadget id="calculator">140 / 320</gadget>
<output>7/16 = around 0.4375</output>
<gadget id="calculator">(7/16) * 100</gadget>
<output>175/4 = around 43.75</output>
<result>175/4 = around 43.75</result>


water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 55 ° c , what is the temperature of the pot of water in ° f ?

Explanation: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 55 ) / 5 + 32 = 131 ° f the answer is c ."

add(multiply(divide(subtract(212, 32), 100), 55), 32)

<gadget id="calculator">212 - 32</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) * 55</gadget>
<output>99</output>
<gadget id="calculator">99 + 32</gadget>
<output>131</output>
<result>131</result>


what distance will be covered by a bus moving at 126 kmph in 10 seconds ?

Explanation: "126 kmph = 126 * 5 / 18 = 35 mps d = speed * time = 35 * 10 = 350 m . answer : c"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">126 * (5/18)</gadget>
<output>35</output>
<gadget id="calculator">35 * 10</gadget>
<output>350</output>
<result>350</result>


the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is

Explanation: explanation : area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d

multiply(subtract(multiply(multiply(2, add(10, 7)), 5), add(add(multiply(2, 3), multiply(2, 1.5)), multiply(2, 1.5))), 3)

<gadget id="calculator">10 + 7</gadget>
<output>17</output>
<gadget id="calculator">2 * 17</gadget>
<output>34</output>
<gadget id="calculator">34 * 5</gadget>
<output>170</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">2 * 1.5</gadget>
<output>3</output>
<gadget id="calculator">6 + 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 3</gadget>
<output>12</output>
<gadget id="calculator">170 - 12</gadget>
<output>158</output>
<gadget id="calculator">158 * 3</gadget>
<output>474</output>
<result>474</result>


o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :

Explanation: o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 7 + ( - 6 ) + ( - 9 ) + 6 = - 2 the answer is b .

add(add(add(multiply(5.3, const_1), multiply(negate(6.7), const_1)), negate(7.3)), multiply(6.6, const_1))

<gadget id="calculator">5.3 * 1</gadget>
<output>5.3</output>
<gadget id="calculator">-6.7</gadget>
<output>-6.7</output>
<gadget id="calculator">(-6.7) * 1</gadget>
<output>-6.7</output>
<gadget id="calculator">5.3 + (-6.7)</gadget>
<output>-1.4</output>
<gadget id="calculator">-7.3</gadget>
<output>-7.3</output>
<gadget id="calculator">(-1.4) + (-7.3)</gadget>
<output>-8.7</output>
<gadget id="calculator">6.6 * 1</gadget>
<output>6.6</output>
<gadget id="calculator">(-8.7) + 6.6</gadget>
<output>-2.1</output>
<result>-2.1</result>


a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?

Explanation: explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b

add(add(multiply(power(10, const_2), negate(subtract(3, 1))), multiply(subtract(subtract(3, 1), negate(subtract(3, 1))), 10)), 1)

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">100 * (-2)</gadget>
<output>-200</output>
<gadget id="calculator">2 - (-2)</gadget>
<output>4</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">(-200) + 40</gadget>
<output>-160</output>
<gadget id="calculator">(-160) + 1</gadget>
<output>-159</output>
<result>-159</result>


in a certain company , a third of the workers do not have a retirement plan . 40 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?

Explanation: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,6 * 1 / 3 * x 120 = 14 / 30 x x = 257 257 - 120 = 137 answer e"

multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(40, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(40, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(1/3) - (2/15)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(1/5) + (4/15)</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">120 / (7/15)</gadget>
<output>1_800/7 = around 257.142857</output>
<gadget id="calculator">(2/3) - (4/15)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/15) + (2/5)</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">(1_800/7) * (8/15)</gadget>
<output>960/7 = around 137.142857</output>
<result>960/7 = around 137.142857</result>


the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 72.0 billion , a year ago . by what percent did the revenue fall ?

Explanation: "$ 72 - $ 48 = 24 $ ( 24 / 72 ) * 100 = 33.33 % answer : e"

multiply(divide(subtract(72.0, 48.0), 72.0), const_100)

<gadget id="calculator">72 - 48</gadget>
<output>24</output>
<gadget id="calculator">24 / 72</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


a trader bought a car at 10 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 90 s = 90 * ( 180 / 100 ) = 162 100 - 162 = 62 % answer : b"

multiply(subtract(divide(divide(multiply(subtract(const_100, 10), add(const_100, 80)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">90 * 180</gadget>
<output>16_200</output>
<gadget id="calculator">16_200 / 100</gadget>
<output>162</output>
<gadget id="calculator">162 / 100</gadget>
<output>81/50 = around 1.62</output>
<gadget id="calculator">(81/50) - 1</gadget>
<output>31/50 = around 0.62</output>
<gadget id="calculator">(31/50) * 100</gadget>
<output>62</output>
<result>62</result>


a man buys a cycle for rs . 2800 and sells it at a loss of 25 % . what is the selling price of the cycle ?

Explanation: "s . p . = 75 % of rs . 2800 = rs . 75 x 2800 / 100 = rs . 1190 answer : option c"

divide(multiply(subtract(const_100, 25), 2800), const_100)

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 * 2_800</gadget>
<output>210_000</output>
<gadget id="calculator">210_000 / 100</gadget>
<output>2_100</output>
<result>2_100</result>


the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?

Explanation: a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .

multiply(divide(subtract(const_100, 40), add(const_100, 25)), divide(5, 4))

<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">60 / 125</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(12/25) * (5/4)</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


the area of a triangle is with base 10 m and height 5 m ?

Explanation: "1 / 2 * 10 * 5 = 25 m 2 answer : b"

<gadget id="calculator">(10 * 5) / 2</gadget>
<output>25</output>
<result>25</result>


how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?

Explanation: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d"

divide(multiply(subtract(13, const_1), subtract(subtract(13, const_1), const_3)), const_2)

<gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">12 * 9</gadget>
<output>108</output>
<gadget id="calculator">108 / 2</gadget>
<output>54</output>
<result>54</result>


a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?

Explanation: "let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ."

add(divide(subtract(multiply(38, 5), multiply(30, 5)), subtract(42, 38)), 5)

<gadget id="calculator">38 * 5</gadget>
<output>190</output>
<gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">190 - 150</gadget>
<output>40</output>
<gadget id="calculator">42 - 38</gadget>
<output>4</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>15</result>


in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?

Explanation: c 10

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">(5/8) * 16</gadget>
<output>10</output>
<result>10</result>


in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 per kg ?

Explanation: solution required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3 . answer c

divide(subtract(20, 16.5), subtract(16.5, 15))

<gadget id="calculator">20 - 16.5</gadget>
<output>3.5</output>
<gadget id="calculator">16.5 - 15</gadget>
<output>1.5</output>
<gadget id="calculator">3.5 / 1.5</gadget>
<output>2.333333</output>
<result>2.333333</result>


a can do a piece of work in 4 days . b can do it in 10 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?

Explanation: "c = 1 / 2 - 1 / 4 - 1 / 10 = 3 / 20 = > 20 / 3 days answer : b"

divide(multiply(4, 10), divide(subtract(multiply(4, 10), multiply(add(divide(multiply(4, 10), 4), divide(multiply(4, 10), 10)), 2)), 2))

<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">40 - 28</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">40 / 6</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>


a and b invests rs . 1500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?

Explanation: "( 1.5 * 6 + 3 * 6 ) : ( 4 * 12 ) 27 : 48 = > 9 : 16 answer : e"

divide(add(multiply(1500, 6), multiply(multiply(1500, const_2), 6)), multiply(4000, add(6, 6)))

<gadget id="calculator">1_500 * 6</gadget>
<output>9_000</output>
<gadget id="calculator">1_500 * 2</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 * 6</gadget>
<output>18_000</output>
<gadget id="calculator">9_000 + 18_000</gadget>
<output>27_000</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">4_000 * 12</gadget>
<output>48_000</output>
<gadget id="calculator">27_000 / 48_000</gadget>
<output>9/16 = around 0.5625</output>
<result>9/16 = around 0.5625</result>


the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .

Explanation: let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b

add(multiply(divide(subtract(100, const_4), multiply(2, const_4)), 3), 2)

<gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">96 / 8</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<result>38</result>


Explanation: "= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e ."

<gadget id="calculator">24 * 99</gadget>
<output>2_376</output>
<result>2_376</result>


a reduction of 40 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 2400 , what is the reduced price for kg ?

Explanation: "explanation : 2400 * ( 40 / 100 ) = 960 - - - - 8 ? - - - - 1 = > rs . 120 answer : a"

divide(divide(multiply(2400, 40), const_100), 8)

<gadget id="calculator">2_400 * 40</gadget>
<output>96_000</output>
<gadget id="calculator">96_000 / 100</gadget>
<output>960</output>
<gadget id="calculator">960 / 8</gadget>
<output>120</output>
<result>120</result>


a trail mix company keeps costs down by employing the peanuts : cashews : almonds ratio of 10 : 4 : 1 in each bag of up to 75 total nuts . what is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts ?

Explanation: peanuts = 50 cashews = 20 almonds = 5 we want to remove as many peanuts as possible while still having peanuts represent more than half of the mixture . . . the number of cashews and almonds will stay the same though , so we have 20 + 5 = 25 of those non - peanuts in total . if we had 25 peanuts and 25 non - peanuts , then that would be 50 % exactly . we want more than 50 % though , so we need to add in 1 more peanut . this gives us . . . peanuts = 26 cashews = 20 almonds = 5 the question asked for the decrease in the number of peanuts as a percentage . we started with 50 peanuts and removed 24 = 24 / 50 = 48 % ; answer : b

multiply(divide(75, add(add(10, 4), 1)), 10)

<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<gadget id="calculator">14 + 1</gadget>
<output>15</output>
<gadget id="calculator">75 / 15</gadget>
<output>5</output>
<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<result>50</result>


we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?

Explanation: "m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b ."

subtract(90, subtract(390, multiply(90, 4)))

<gadget id="calculator">90 * 4</gadget>
<output>360</output>
<gadget id="calculator">390 - 360</gadget>
<output>30</output>
<gadget id="calculator">90 - 30</gadget>
<output>60</output>
<result>60</result>


a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?

Explanation: "133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c ."

<gadget id="calculator">133 + 16</gadget>
<output>149</output>
<gadget id="calculator">149 % 50</gadget>
<output>49</output>
<result>49</result>


the length of a rectangular floor is more than its breadth by 200 % . if rs . 240 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 240 / 3 = 80 sq m l b = 80 i . e . , l * l / 3 = 240 l 2 = 240 = > l = 15.49 answer : d"

multiply(sqrt(divide(divide(240, 3), const_3)), const_3)

<gadget id="calculator">240 / 3</gadget>
<output>80</output>
<gadget id="calculator">80 / 3</gadget>
<output>80/3 = around 26.666667</output>
<gadget id="calculator">(80/3) ** (1/2)</gadget>
<output>4*sqrt(15)/3 = around 5.163978</output>
<gadget id="calculator">(4*sqrt(15)/3) * 3</gadget>
<output>4*sqrt(15) = around 15.491933</output>
<result>4*sqrt(15) = around 15.491933</result>


if the cost price of 50 articles is equal to the selling price of 40 articles , then the gain or loss percent is ?

Explanation: "c 25 % given that , cost price of 50 article is equal to selling price of 40 articles . let cost price of one article = rs . 1 selling price of 40 articles = rs . 50 but cost price of 40 articles = rs . 40 therefore , the trader made profit . \ percentage of profit = 10 / 40 * 100 = 25 %"

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 40), 50)), divide(multiply(const_100, 40), 50)))

<gadget id="calculator">100 * 40</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 50</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">20 / 80</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">100 * (1/4)</gadget>
<output>25</output>
<result>25</result>


if 1 / ( x + 1 ) + 1 / ( x - 1 ) = 1 / ( x - 1 ) , what is the value of x ?

Explanation: if we solve the question , we get x = 1 . option : c

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<result>1</result>


Explanation: b 5050 you must have noticed that 50 pairs of n ^ 2 – ( n - 1 ) ^ 2 exist . n ^ 2 – ( n - 1 ) ^ 2 = n + ( n – 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050

divide(multiply(100, add(100, const_1)), const_2)

<gadget id="calculator">100 + 1</gadget>
<output>101</output>
<gadget id="calculator">100 * 101</gadget>
<output>10_100</output>
<gadget id="calculator">10_100 / 2</gadget>
<output>5_050</output>
<result>5_050</result>


the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is

Explanation: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."

divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100))

<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">39.4 - 19.4</gadget>
<output>20</output>
<gadget id="calculator">20 / 1_000</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>


there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ?

Explanation: "7 = 3 blue balls + 12 / 3 answer : d"

<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<result>7</result>


the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?

Explanation: arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer .

divide(subtract(multiply(8, 43.1), 158.4), divide(8, const_2))

<gadget id="calculator">8 * 43.1</gadget>
<output>344.8</output>
<gadget id="calculator">344.8 - 158.4</gadget>
<output>186.4</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">186.4 / 4</gadget>
<output>46.6</output>
<result>46.6</result>


the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 45 kms . what was the total distance traveled in 12 hours ?

Explanation: explanation : total distance travelled in 12 hours = ( 45 + 47 + 49 + . . . . . upto 12 terms ) this is an a . p with first term , a = 45 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 45 + { 12 - 1 ) x 2 ] = 6 ( 112 ) = 672 kms . answer : c

multiply(add(multiply(2, 45), multiply(subtract(12, const_1), 2)), divide(12, 2))

<gadget id="calculator">2 * 45</gadget>
<output>90</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">90 + 22</gadget>
<output>112</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">112 * 6</gadget>
<output>672</output>
<result>672</result>


n denotes the number obtained when n is rounded to the nearest tenth . for example 4.31 = 4.3 0.089 - 1.135 =

Explanation: here let the first quantity be a = > a rounded to nearest tenths = > 0.1 similarly let the second quantity be b = > b rounded to nearest tenths = > 1.1 = > a - b = 0.1 - 1.1 = - 1 hence a - b = - 1 answer : d

<gadget id="calculator">0.089 - 1.135</gadget>
<output>-1.046</output>
<result>-1.046</result>


initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many w women are currently in the room ?

Explanation: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"

multiply(2, subtract(divide(multiply(5, subtract(14, 2)), 4), 3))

<gadget id="calculator">14 - 2</gadget>
<output>12</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<result>24</result>


a certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?

Explanation: general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 45 − 30 / 30 ∗ 100 = 50 answer : c .

multiply(divide(subtract(45, 30), 30), const_100)

<gadget id="calculator">45 - 30</gadget>
<output>15</output>
<gadget id="calculator">15 / 30</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


a bus trip of 660 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?

Explanation: "the time is the distance / speed . the time difference is 1 hour . 660 / v - 660 / ( v + 5 ) = 1 660 ( v + 5 ) - 660 v = ( v ) ( v + 5 ) 3300 = ( v ) ( v + 5 ) 55 * 60 = ( v ) ( v + 5 ) v = 55 mph the answer is d ."

divide(subtract(sqrt(add(multiply(multiply(660, 5), const_4), power(5, const_2))), 5), const_2)

<gadget id="calculator">660 * 5</gadget>
<output>3_300</output>
<gadget id="calculator">3_300 * 4</gadget>
<output>13_200</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">13_200 + 25</gadget>
<output>13_225</output>
<gadget id="calculator">13_225 ** (1/2)</gadget>
<output>115</output>
<gadget id="calculator">115 - 5</gadget>
<output>110</output>
<gadget id="calculator">110 / 2</gadget>
<output>55</output>
<result>55</result>


in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .

Explanation: the number of students with first division = 30 % of 300 = 30 / 100 × 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 90 + 162 ) = 48 answer : e

divide(multiply(300, subtract(const_100, add(30, 54))), const_100)

<gadget id="calculator">30 + 54</gadget>
<output>84</output>
<gadget id="calculator">100 - 84</gadget>
<output>16</output>
<gadget id="calculator">300 * 16</gadget>
<output>4_800</output>
<gadget id="calculator">4_800 / 100</gadget>
<output>48</output>
<result>48</result>


5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men â € ™ s wages are ?

Explanation: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e"

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">45 / 15</gadget>
<output>3</output>
<result>3</result>


two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?

Explanation: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible two dice are rolled , n ( s ) = 6 × 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6

multiply(multiply(divide(const_1, multiply(const_2, const_3)), divide(const_1, multiply(const_2, const_3))), multiply(const_2, const_3))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * (1/6)</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">(1/36) * 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


if x is 12 percent greater than 80 , then x =

Explanation: "12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a ."

add(80, multiply(divide(12, const_100), 80))

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 80</gadget>
<output>48/5 = around 9.6</output>
<gadget id="calculator">80 + (48/5)</gadget>
<output>448/5 = around 89.6</output>
<result>448/5 = around 89.6</result>


a and b complete a work in 6 days . a alone can do it in 8 days . if both together can do the work in how many days ?

Explanation: "1 / 6 + 1 / 8 = 7 / 24 24 / 7 = 3.43 days answer : b"

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/6) + (1/8)</gadget>
<output>7/24 = around 0.291667</output>
<gadget id="calculator">1 / (7/24)</gadget>
<output>24/7 = around 3.428571</output>
<result>24/7 = around 3.428571</result>


130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?

Explanation: "quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c"

add(multiply(divide(130, add(2, 3)), 3), multiply(divide(160, add(3, 4)), 3))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">130 / 5</gadget>
<output>26</output>
<gadget id="calculator">26 * 3</gadget>
<output>78</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">160 / 7</gadget>
<output>160/7 = around 22.857143</output>
<gadget id="calculator">(160/7) * 3</gadget>
<output>480/7 = around 68.571429</output>
<gadget id="calculator">78 + (480/7)</gadget>
<output>1_026/7 = around 146.571429</output>
<result>1_026/7 = around 146.571429</result>


a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 5 days and b leaves after 3 days from the beginning . how long will work lost ?

Explanation: "5 / 10 + 3 / 15 + x / 20 = 1 x = 18 / 3 = 6 answer : d"

add(divide(subtract(const_1, add(multiply(subtract(3, 5), add(inverse(15), inverse(20))), multiply(add(inverse(20), add(inverse(10), inverse(15))), 5))), inverse(15)), const_4.0)

<gadget id="calculator">3 - 5</gadget>
<output>-2</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(-2) * (7/60)</gadget>
<output>-7/30 = around -0.233333</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + (1/15)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/20) + (1/6)</gadget>
<output>13/60 = around 0.216667</output>
<gadget id="calculator">(13/60) * 5</gadget>
<output>13/12 = around 1.083333</output>
<gadget id="calculator">(-7/30) + (13/12)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">1 - (17/20)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) / (1/15)</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(9/4) + 4</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>


at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?

Explanation: "system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86"

divide(multiply(40, 3), divide(35, const_100))

<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">120 / (7/20)</gadget>
<output>2_400/7 = around 342.857143</output>
<result>2_400/7 = around 342.857143</result>


the length of the bridge , which a train 130 metres long and travelling at 54 km / hr can cross in 30 seconds , is :

Explanation: "speed = [ 54 x 5 / 18 ] m / sec = [ 15 / 1 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) = 450 = > x = 450 - 130 = 320 m answer : c"

subtract(multiply(divide(multiply(54, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">54_000 / 3_600</gadget>
<output>15</output>
<gadget id="calculator">15 * 30</gadget>
<output>450</output>
<gadget id="calculator">450 - 130</gadget>
<output>320</output>
<result>320</result>


the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than

Explanation: "given that a + b = 16 + b + c = > a â € “ c = 16 + b â € “ b = 16 = > c is younger than a by 16 years answer : d"

<gadget id="calculator">16 * 1</gadget>
<output>16</output>
<result>16</result>


the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 ° is ?

Explanation: 30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c

divide(multiply(multiply(30, const_pi), power(12, const_2)), const_360)

<gadget id="calculator">30 * pi</gadget>
<output>30*pi = around 94.24778</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">(30*pi) * 144</gadget>
<output>4320*pi = around 13_571.680264</output>
<gadget id="calculator">(4320*pi) / 360</gadget>
<output>12*pi = around 37.699112</output>
<result>12*pi = around 37.699112</result>


find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e"

multiply(divide(subtract(1360, 15), subtract(6, const_1)), 6)

<gadget id="calculator">1_360 - 15</gadget>
<output>1_345</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_345 / 5</gadget>
<output>269</output>
<gadget id="calculator">269 * 6</gadget>
<output>1_614</output>
<result>1_614</result>


solve the equation 2 – x = 2 b – 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7

Explanation: solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 ≠ 0 , i . e . a ≠ 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b ≠ 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) ≠ 0 in this case the equation has no solution . if b = 7 and a ≠ 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>1</result>


in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .

Explanation: let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c .

subtract(224, subtract(add(add(multiply(50, const_2), multiply(45, const_4)), multiply(8, const_4)), add(add(50, 45), 8)))

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">100 + 180</gadget>
<output>280</output>
<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">280 + 32</gadget>
<output>312</output>
<gadget id="calculator">50 + 45</gadget>
<output>95</output>
<gadget id="calculator">95 + 8</gadget>
<output>103</output>
<gadget id="calculator">312 - 103</gadget>
<output>209</output>
<gadget id="calculator">224 - 209</gadget>
<output>15</output>
<result>15</result>


a motorcyclist goes from bombay to pune , a distance of 160 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?

Explanation: "t = 160 / 32 = 5 h t = 5 - 3 = 2 time ratio = 5 : 2 = 5 : 2 speed ratio = 2 : 5 answer : b"

divide(divide(160, divide(160, 32)), divide(160, subtract(divide(160, 32), const_3)))

<gadget id="calculator">160 / 32</gadget>
<output>5</output>
<gadget id="calculator">160 / 5</gadget>
<output>32</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">160 / 2</gadget>
<output>80</output>
<gadget id="calculator">32 / 80</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?

Explanation: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d"

multiply(subtract(power(add(const_1, divide(40, const_100)), const_2), const_1), const_100)

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(7/5) ** 2</gadget>
<output>49/25 = around 1.96</output>
<gadget id="calculator">(49/25) - 1</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">(24/25) * 100</gadget>
<output>96</output>
<result>96</result>


how many shots of 1 cm radius can be prepared from a sphere of 5 cm radius ?

Explanation: 4 / 3 ï € * 5 * 5 * 5 = 4 / 3 ï € * 1 * 1 * 1 * x x = 125 answer : d

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>


in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .

Explanation: next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b

power(add(power(multiply(subtract(1, divide(1, 10)), 150), const_2), power(subtract(power(add(power(150, const_2), power(90, const_2)), divide(1, 2)), multiply(subtract(1, divide(1, 10)), 150)), const_2)), divide(1, 2))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 150</gadget>
<output>135</output>
<gadget id="calculator">135 ** 2</gadget>
<output>18_225</output>
<gadget id="calculator">150 ** 2</gadget>
<output>22_500</output>
<gadget id="calculator">90 ** 2</gadget>
<output>8_100</output>
<gadget id="calculator">22_500 + 8_100</gadget>
<output>30_600</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">30_600 ** (1/2)</gadget>
<output>30*sqrt(34) = around 174.928557</output>
<gadget id="calculator">(30*sqrt(34)) - 135</gadget>
<output>-135 + 30*sqrt(34) = around 39.928557</output>
<gadget id="calculator">(-135 + 30*sqrt(34)) ** 2</gadget>
<output>(-135 + 30*sqrt(34))**2 = around 1_594.289652</output>
<gadget id="calculator">18_225 + ((-135 + 30*sqrt(34))**2)</gadget>
<output>(-135 + 30*sqrt(34))**2 + 18225 = around 19_819.289652</output>
<gadget id="calculator">((-135 + 30*sqrt(34))**2 + 18225) ** (1/2)</gadget>
<output>sqrt((-135 + 30*sqrt(34))**2 + 18225) = around 140.780999</output>
<result>sqrt((-135 + 30*sqrt(34))**2 + 18225) = around 140.780999</result>


a train 124 m long running at 68 kmph crosses a platform in 19 sec . what is the length of the platform ?

Explanation: "d = 68 * 5 / 18 = 19 = 358 – 124 = 234 answer : b"

subtract(multiply(19, multiply(68, const_0_2778)), 124)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">68 * (5/18)</gadget>
<output>170/9 = around 18.888889</output>
<gadget id="calculator">19 * (170/9)</gadget>
<output>3_230/9 = around 358.888889</output>
<gadget id="calculator">(3_230/9) - 124</gadget>
<output>2_114/9 = around 234.888889</output>
<result>2_114/9 = around 234.888889</result>


the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .

Explanation: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d"

<gadget id="calculator">42 * 12</gadget>
<output>504</output>
<result>504</result>


sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 468 per week . how much does she earn in dollars per hour ?

Explanation: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 468 . hourly wage = 468 / 36 = 13 answer : e"

divide(468, add(multiply(8, const_3), multiply(6, const_2)))

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">468 / 36</gadget>
<output>13</output>
<result>13</result>


a trader bought a car at 20 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 80 s = 80 * ( 150 / 100 ) = 120 100 - 120 = 20 % answer : c"

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 50)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">80 * 150</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) - 1</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?

Explanation: p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d .

multiply(divide(add(const_4, const_4), 17), divide(subtract(add(const_4, const_4), 1), subtract(17, 1)))

<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">8 / 17</gadget>
<output>8/17 = around 0.470588</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">17 - 1</gadget>
<output>16</output>
<gadget id="calculator">7 / 16</gadget>
<output>7/16 = around 0.4375</output>
<gadget id="calculator">(8/17) * (7/16)</gadget>
<output>7/34 = around 0.205882</output>
<result>7/34 = around 0.205882</result>


aarti can do a piece of work in 9 days . in how many days will she complete three time of work of same type ?

Explanation: "we have the important relation , more work , more time ( days ) a piece of work can be done in 9 days . three times of work of same type can be done in 9 x 3 = 27 days answer d"

<gadget id="calculator">3 * 9</gadget>
<output>27</output>
<result>27</result>


what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?

Explanation: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."

add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1)

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<gadget id="calculator">13 * 2</gadget>
<output>26</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>


there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .

Explanation: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 7 and for second = 6 so total methods = 7 * 6 = 42 answer : e"

<gadget id="calculator">binomial(7, 2)</gadget>
<output>21</output>
<gadget id="calculator">21 + 21</gadget>
<output>42</output>
<result>42</result>


when a stone is dropped from a building 200 m high , its speed is proportional to the time elapsed after dropping . the distance traveled is proportional to the square of the time elapsed . after 1 second the speed of the train was 10 m / sec and it was 190 m above the ground . when its speed is 25 m / sec , what would be its distance from the ground ?

Explanation: v = x * t and s = y * t ^ 2 10 = x * 1 , hence x = 10 units ( 200 - 190 ) = y * 1 * 1 y = 10 when speed = 25 m / sec , time elapsed = 25 / 10 = 2.5 sec distance travelled by stone = 10 * ( 2.5 ) ^ 2 = 62.5 mts so distance of stone above ground = 200 - 62.5 = 137.5 mtrs answer : b

subtract(200, multiply(power(divide(25, subtract(200, 190)), const_2), 10))

<gadget id="calculator">200 - 190</gadget>
<output>10</output>
<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) ** 2</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) * 10</gadget>
<output>125/2 = around 62.5</output>
<gadget id="calculator">200 - (125/2)</gadget>
<output>275/2 = around 137.5</output>
<result>275/2 = around 137.5</result>


in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?

Explanation: let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a

multiply(divide(26, subtract(const_1, add(add(divide(1, 4), divide(1, 8)), divide(1, 12)))), divide(1, 8))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/4) + (1/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(3/8) + (1/12)</gadget>
<output>11/24 = around 0.458333</output>
<gadget id="calculator">1 - (11/24)</gadget>
<output>13/24 = around 0.541667</output>
<gadget id="calculator">26 / (13/24)</gadget>
<output>48</output>
<gadget id="calculator">48 * (1/8)</gadget>
<output>6</output>
<result>6</result>


a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 250 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?

Explanation: "the distance between the nest and the ditch is 250 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 250 = 7500 . d = st 7500 / 1.5 = t , i think we can take 7500 meters as 7.5 km , then only we get t = 5 . ( 1000 meters = 1 km ) d )"

divide(divide(multiply(250, multiply(15, const_2)), const_1000), divide(15, const_10))

<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">250 * 30</gadget>
<output>7_500</output>
<gadget id="calculator">7_500 / 1_000</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(15/2) / (3/2)</gadget>
<output>5</output>
<result>5</result>


solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?

Explanation: "15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b ."

multiply(divide(subtract(15, 10), subtract(30, 15)), 300)

<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">5 / 15</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 300</gadget>
<output>100</output>
<result>100</result>


on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 40 percent . what was the total rent the motel actually charged for that night ?

Explanation: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 40 % . 4 x = 200 = > x = 500 answer a"

divide(multiply(10, subtract(60, 40)), divide(40, const_100))

<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>500</result>


the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?

Explanation: "a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b"

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">81 * 8</gadget>
<output>648</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">648 / (1/2)</gadget>
<output>1_296</output>
<gadget id="calculator">1_296 ** (1/2)</gadget>
<output>36</output>
<result>36</result>


how much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m , moving at 36 kmph in the same direction ?

Explanation: "the distance to be covered = sum of their lengths = 380 + 540 = 920 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 920 / 10 = 92 sec . answer : d"

divide(add(380, 540), multiply(subtract(72, 36), const_0_2778))

<gadget id="calculator">380 + 540</gadget>
<output>920</output>
<gadget id="calculator">72 - 36</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">920 / 10</gadget>
<output>92</output>
<result>92</result>


let the number which when multiplied by 16 is increased by 375 .

Explanation: "solution let the number be x . then , 16 x - x = 375 ‹ = › 15 x = 375 x ‹ = › 25 . answer d"

<gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">375 / 15</gadget>
<output>25</output>
<result>25</result>


jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?

Explanation: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e

multiply(divide(14, add(const_1, add(const_0_25, divide(const_1, const_2)))), const_3)

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 + (3/4)</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">14 / (7/4)</gadget>
<output>8</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<result>24</result>


a cricket player whose bowling average was 21.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?

Explanation: "average = total runs / total wickets total runs after last match = 21.5 w + 52 total wickets after last match = w + 5 ( 21.5 w + 52 ) / ( w + 5 ) = 21.5 - 0.5 = 21 w = 106 so total wickets aftr last match = w + 5 = 111 answer : c"

divide(subtract(multiply(subtract(21.5, 0.5), 5), 52), 0.5)

<gadget id="calculator">21.5 - 0.5</gadget>
<output>21</output>
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">105 - 52</gadget>
<output>53</output>
<gadget id="calculator">53 / 0.5</gadget>
<output>106</output>
<result>106</result>


8 men , working 8 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?

Explanation: "the number of hours required to complete the work is 8 * 8 * 18 = 1152 12 × 12 × ( x ) = 1152 x = 8 the answer is c ."

divide(multiply(multiply(8, 8), 18), multiply(12, 12))

<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 * 18</gadget>
<output>1_152</output>
<gadget id="calculator">12 * 12</gadget>
<output>144</output>
<gadget id="calculator">1_152 / 144</gadget>
<output>8</output>
<result>8</result>


if 3 men or 4 women can do a piece of work in 16 days , in how many days can 12 men and 8 women do the same piece of work ?

Explanation: "3 men can finish a work in 16 days , so in 1 day 3 men finish 1 / 16 th of work and in 1 day 1 men can finish , 1 / 48 th of work . similarly , in 1 day 1 women can finish 1 / 64 th of work . 12 men in 1 day can finish , 12 / 48 = 1 / 4 , 8 women in 1 day can finish = 8 / 64 = 1 / 8 1 / 4 + 1 / 8 = 3 / 8 . hence number of days to complete is 8 / 3 days . answer : a"

inverse(add(divide(12, multiply(3, 16)), divide(8, multiply(4, 16))))

<gadget id="calculator">3 * 16</gadget>
<output>48</output>
<gadget id="calculator">12 / 48</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">4 * 16</gadget>
<output>64</output>
<gadget id="calculator">8 / 64</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/4) + (1/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">1 / (3/8)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>


john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?

Explanation: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e

subtract(add(multiply(const_100, const_10), 600), divide(add(600, add(multiply(const_100, const_10), 600)), const_2))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>
<gadget id="calculator">600 + 1_600</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 2</gadget>
<output>1_100</output>
<gadget id="calculator">1_600 - 1_100</gadget>
<output>500</output>
<result>500</result>


a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?

Explanation: solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c

<gadget id="calculator">800 + 1_000</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 + 1_200</gadget>
<output>3_000</output>
<gadget id="calculator">1_000 / 3_000</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1_200 * (1/3)</gadget>
<output>400</output>
<result>400</result>


the speed of a car is 85 km in the first hour and 45 km in the second hour . what is the average speed of the car ?

Explanation: s = ( 85 + 45 ) / 2 = 65 kmph answer : b

<gadget id="calculator">85 + 45</gadget>
<output>130</output>
<gadget id="calculator">130 / 2</gadget>
<output>65</output>
<result>65</result>


the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?

Explanation: trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d .

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

Explanation: "the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b"

<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<result>300</result>


carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?

Explanation: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b"

<gadget id="calculator">2 + 10</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 10</gadget>
<output>34</output>
<gadget id="calculator">34 + 10</gadget>
<output>44</output>
<gadget id="calculator">44 / 12</gadget>
<output>11/3 = around 3.666667</output>
<result>11/3 = around 3.666667</result>


points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?

Explanation: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a"

divide(divide(power(const_4, const_2), const_2), divide(power(add(const_10, const_2), const_2), const_2))

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">144 / 2</gadget>
<output>72</output>
<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


the cash difference between the selling prices of an article at a profit of 4 % and 2 % is rs . 3 . the ratio of the two selling prices is ?

Explanation: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 102 % of x = 104 / 102 = 52 / 51 = 52 : 51 answer : a"

divide(add(const_100, 4), add(const_100, 2))

<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">104 / 102</gadget>
<output>52/51 = around 1.019608</output>
<result>52/51 = around 1.019608</result>


two whole numbers whose sum is 100 can not be in the ratio

Explanation: d ) 2 : 6

divide(divide(subtract(divide(100, const_2), const_10), const_2), add(divide(100, const_2), const_10))

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">50 + 10</gadget>
<output>60</output>
<gadget id="calculator">20 / 60</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


in a certain warehouse , 30 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?

Explanation: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 30 % of the packages weigh less than 75 pounds so , 30 % oft = number of packages that weigh less than 75 pounds 30 % of 240 = 72 , so 72 packages weigh less than 75 pounds of those 72 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 72 - 48 = 24 = c"

subtract(divide(multiply(multiply(divide(48, subtract(const_100, 80)), const_100), 30), const_100), 48)

<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">48 / 20</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 100</gadget>
<output>240</output>
<gadget id="calculator">240 * 30</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 100</gadget>
<output>72</output>
<gadget id="calculator">72 - 48</gadget>
<output>24</output>
<result>24</result>


a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10 . in all papers together , the candidate obtained 60 % of the total marks then , the number of papers in which he got more than 50 % marks is

Explanation: solution : let the marks obtained in five subjects be 6 x , 7 x , 8 x , 9 x and 10 x . total marks obtained = 40 x max . marks of the five subjects = 40 x / 0.6 [ 40 x is 60 % of total marks ] max . marks in each subject = 40 x / 0.6 * 5 = 13.33 x hence , % of each subject = 6 x * 100 / 13.33 = 45.01 % or , 7 x * 100 / 13.33 = 52.51 in same way other percentage are 60.01 % , 67.52 % , 75.01 % . hence , number of subjects in which he gets more than 50 % marks = 4 . answer : option c

<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>4</result>


subtracting 5 % of a from a is equivalent to multiplying a by how much ?

Explanation: "answer let a - 5 % of a = ab . ⇒ ( 95 x a ) / 100 = ab ∴ b = 0.95 correct option : a"

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<result>19/20 = around 0.95</result>


a bag consists of 20 marbles , of which 5 are blue , 7 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?

Explanation: "bag consists of 20 marbles , of which 5 are blue , 7 are red remainder are white . so , white = 20 - 5 - 7 = 8 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 7 / 20 + 8 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."

divide(add(subtract(20, add(5, 7)), 7), 20)

<gadget id="calculator">5 + 7</gadget>
<output>12</output>
<gadget id="calculator">20 - 12</gadget>
<output>8</output>
<gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>


a trader bought a car at 20 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 80 s = 80 * ( 160 / 100 ) = 128 100 - 128 = 28 % answer : a"

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 60)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">80 * 160</gadget>
<output>12_800</output>
<gadget id="calculator">12_800 / 100</gadget>
<output>128</output>
<gadget id="calculator">128 / 100</gadget>
<output>32/25 = around 1.28</output>
<gadget id="calculator">(32/25) - 1</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>28</result>


how many seconds will a 550 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 550 * 3 / 50 = 33 sec . answer : c"

divide(550, multiply(subtract(63, 3), const_0_2778))

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">550 / (50/3)</gadget>
<output>33</output>
<result>33</result>


jansi went out for shopping . she had in her handbag approximately rs . 15 / - in one rupee notes and 20 p . coins . when she returned she had as many one rupee notes as she originally had and as many 20 p . coins as she originally had one rupee notes . she actually came back with about one - third of what she had started out with . how much did she spend and exactly how much did she have with her when she started out ?

Explanation: a 9.60 let us assume that originally jansi had x rupees and y 20 paise coins . going shopping she had ( 100 x + 20 y ) paise . she returned with only ( 100 y + 20 x ) paise . this last sum , as we know , is one - third of the original and therefore 3 ( 100 y + 20 x ) = 100 x + 20 y simplifying we have x = 7 y if y is 1 thenx is 7 . assuming this so jansi had 7.20 rupees when she set out for shopping . this is wrong because jansi actually had about 15 rupees . let us see now what we get if y = 2 . then x = 14 . the original sum was 14.40 rupees which accords with the condition of the problem . if we assume that y = 3 then the sum will be too big — 21.60 rupees . therefore the only suitable answer is 14.40 rupees . after shopping jansi had 2 one rupee notes and 14 twenty paise coins . this is actually l / 3 rd of the original sum 1,440 : 3 = 480 . jansi ' s purchases , therefore , cost 14.40 — 4.80 = rs 9.60

subtract(add(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20)))), divide(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), 20), const_100)), multiply(add(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20)))), divide(multiply(floor(divide(15, divide(subtract(multiply(const_3, const_100), 20), subtract(const_100, multiply(const_3, 20))))), 20), const_100)), divide(const_1, const_3)))

<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">300 - 20</gadget>
<output>280</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">280 / 40</gadget>
<output>7</output>
<gadget id="calculator">15 / 7</gadget>
<output>15/7 = around 2.142857</output>
<gadget id="calculator">floor(15/7)</gadget>
<output>2</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<gadget id="calculator">2 * 20</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">14 + (2/5)</gadget>
<output>72/5 = around 14.4</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(72/5) * (1/3)</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(72/5) - (24/5)</gadget>
<output>48/5 = around 9.6</output>
<result>48/5 = around 9.6</result>


at a certain organisation , the number of male members went up by 15 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?

Explanation: "men increase by 15 % = = > 1.15 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.15 m + 0.94 f = 1.012 * ( m + f ) 1.15 m + 0.94 f = 1.012 m + 1.012 f 1.15 m - 1.012 m = 1.012 f - 0.94 f 0.138 m = 0.072 f m / f = ( 0.072 ) / ( 0.138 ) = 72 / 138 = 1 / 2 answer = ( a )"

divide(subtract(multiply(add(const_1, divide(1.2, const_100)), const_1000), multiply(subtract(const_1, divide(6, const_100)), const_1000)), subtract(multiply(add(const_1, divide(15, const_100)), const_1000), multiply(add(const_1, divide(1.2, const_100)), const_1000)))

<gadget id="calculator">1.2 / 100</gadget>
<output>0.012</output>
<gadget id="calculator">1 + 0.012</gadget>
<output>1.012</output>
<gadget id="calculator">1.012 * 1_000</gadget>
<output>1_012</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">1 - (3/50)</gadget>
<output>47/50 = around 0.94</output>
<gadget id="calculator">(47/50) * 1_000</gadget>
<output>940</output>
<gadget id="calculator">1_012 - 940</gadget>
<output>72</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">(23/20) * 1_000</gadget>
<output>1_150</output>
<gadget id="calculator">1_150 - 1_012</gadget>
<output>138</output>
<gadget id="calculator">72 / 138</gadget>
<output>12/23 = around 0.521739</output>
<result>12/23 = around 0.521739</result>


in a party every person shakes hands with every other person . if there were a total of 120 handshakes in the party then what is the number of persons present in the party ?

Explanation: "explanation : let the number of persons be n ∴ total handshakes = nc 2 = 120 n ( n - 1 ) / 2 = 120 ∴ n = 16 answer : option b"

divide(add(sqrt(add(multiply(multiply(120, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">240 * 4</gadget>
<output>960</output>
<gadget id="calculator">960 + 1</gadget>
<output>961</output>
<gadget id="calculator">961 ** (1/2)</gadget>
<output>31</output>
<gadget id="calculator">31 + 1</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>


a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 21 inches and the width of the wall is 28 inches , what is the length of the wall , in inches ?

Explanation: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 21 ^ 2 = 441 . area of rectangle is double of that 2 * 441 = 882 . now a = lw and we need find w so a / l = w ; 882 / 28 = 31.5 answer ! answer is b"

<gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">2 * 441</gadget>
<output>882</output>
<gadget id="calculator">882 / 28</gadget>
<output>63/2 = around 31.5</output>
<result>63/2 = around 31.5</result>


when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 96.15 , what is the value of y ?

Explanation: "by the definition of a remainder , the remainder here is equal to 6 / y . the remainder in decimal form is given as . 15 therefore , 6 / y = . 15 solve for y and get 40 . c"

<gadget id="calculator">floor(96.15)</gadget>
<output>96</output>
<gadget id="calculator">96.15 - 96</gadget>
<output>0.15</output>
<gadget id="calculator">6 / 0.15</gadget>
<output>40</output>
<result>40</result>


if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 276 games will be played during the tournament . find the number of participants .

Explanation: "let p be the number of participants . pc 2 = 276 ( p ) ( p - 1 ) = 552 = 24 * 23 p = 24 the answer is c ."

divide(add(sqrt(add(multiply(multiply(276, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">276 * 2</gadget>
<output>552</output>
<gadget id="calculator">552 * 4</gadget>
<output>2_208</output>
<gadget id="calculator">2_208 + 1</gadget>
<output>2_209</output>
<gadget id="calculator">2_209 ** (1/2)</gadget>
<output>47</output>
<gadget id="calculator">47 + 1</gadget>
<output>48</output>
<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<result>24</result>


3 friends had dinner at a restaurant . when the bill was received , akshitha paid 3 / 4 as much as veena paid and veena paid 1 / 2 as much as lasya paid . what fraction of the bill did veena pay ?

Explanation: let veena paid x , so akshitha paid 3 x / 4 , and lasya paid 2 x , so total bill paid is given by x + ( 3 x / 4 ) + 2 x = 1 , we get i . e . x = 4 / 15 answer : a

divide(4, add(add(3, 4), multiply(4, 2)))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">4 / 15</gadget>
<output>4/15 = around 0.266667</output>
<result>4/15 = around 0.266667</result>


a number x is 5 times another number y . the percentage that y is less than x is

Explanation: "say y = 1 and x = 5 . then y = 1 is less than x = 5 by ( 5 - 1 ) / 5 * 100 = 4 / 5 * 100 = 80 % . answer : c ."

multiply(divide(subtract(5, const_1), 5), const_100)

<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 30 % . what percent of the projected revenue was the actual revenue ?

Explanation: last year revenue = 100 ( assume ) ; this year revenue = 70 ; projected revenue = 140 . actual / projected * 100 = 70 / 140 * 100 = 50 % . answer : a .

multiply(divide(subtract(const_100, 30), add(40, const_100)), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">40 + 100</gadget>
<output>140</output>
<gadget id="calculator">70 / 140</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 9 m x 6 m x 22.5 cm ?

Explanation: "number of bricks = volume of wall / volume of bricks = 900 x 600 x 22.5 / 25 x 11.25 x 6 = = 7200 answer : d"

divide(multiply(multiply(multiply(9, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">900 * 600</gadget>
<output>540_000</output>
<gadget id="calculator">540_000 * 22.5</gadget>
<output>12_150_000</output>
<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>
<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>
<gadget id="calculator">12_150_000 / 1_687.5</gadget>
<output>7_200</output>
<result>7_200</result>


at a certain restaurant , the average ( arithmetic mean ) number of customers served for the past x days was 65 . if the restaurant serves 120 customers today , raising the average to 90 customers per day , what is the value of x ?

Explanation: withoutusing the formula , we can see that today the restaurant served 30 customers above the average . the total amount above the average must equal total amount below the average . this additional 30 customers must offset the “ deficit ” below the average of 90 created on the x days the restaurant served only 60 customers per day . 30 / 30 = 1 day . choice ( a ) . withthe formula , we can set up the following : 90 = ( 60 x + 120 ) / ( x + 1 ) 90 x + 90 = 60 x + 120 30 x = 30 x = 1 answer choice ( a )

subtract(divide(subtract(120, 90), subtract(90, 65)), divide(subtract(120, const_100), const_100))

<gadget id="calculator">120 - 90</gadget>
<output>30</output>
<gadget id="calculator">90 - 65</gadget>
<output>25</output>
<gadget id="calculator">30 / 25</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(6/5) - (1/5)</gadget>
<output>1</output>
<result>1</result>


stacy has a 63 page history paper due in 7 days . how many pages per day would she have to write to finish on time ?

Explanation: "63 / 7 = 9 a . 9"

<gadget id="calculator">63 / 7</gadget>
<output>9</output>
<result>9</result>