a room is a square of side 50 feet . a second room is of area 100 square yards . a third room is of area 200 square feet . which of these can seat maximum people ? ( hint : 1 yard = 3 feet )

Explanation: first room because area 50 * 50 = 2500 sq feet second room area 100 sq yard in feet 300 sq feet third room area 200 sq feet answer : a

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<result>200</result>


alex and brian start a business with rs . 7000 each , and after 8 months , brian withdraws half of his capital . how should they share the profits at the end of the 18 months ?

Explanation: alex invests rs . 7000 for 18 months , but brian invests rs . 7000 for the first 8 months and then withdraws rs . 3500 . so , the investment of brian for remaining 10 months is rs . 3500 only . alex : brian 7000 * 18 : ( 7000 * 8 ) + ( 3500 * 10 ) 126000 : 91000 alex : brian = 18 : 13 answer : e

<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">18 / 13</gadget>
<output>18/13 = around 1.384615</output>
<result>18/13 = around 1.384615</result>


of the people who responded to a market survey , 240 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 6 to 1 , how many people responded to the survey ?

Explanation: "ratio = 6 : 1 = > 6 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 240 = > 6 x = 240 = > x = 40 hence total no . of respondents = 240 + 40 = 280 hence c is the answer ."

<gadget id="calculator">240 / 6</gadget>
<output>40</output>
<gadget id="calculator">40 + 240</gadget>
<output>280</output>
<result>280</result>


two trains 119 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?

Explanation: "t = ( 119 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.05 answer : e"

<gadget id="calculator">119 + 165</gadget>
<output>284</output>
<gadget id="calculator">80 + 65</gadget>
<output>145</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">145 * (5/18)</gadget>
<output>725/18 = around 40.277778</output>
<gadget id="calculator">284 / (725/18)</gadget>
<output>5_112/725 = around 7.051034</output>
<result>5_112/725 = around 7.051034</result>


if an integer e is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that e ( e + 1 ) ( e + 2 ) will be divisible by 8 ?

Explanation: for e total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d

divide(add(multiply(divide(divide(96, 8), 8), 2), 2), 8)

<gadget id="calculator">96 / 8</gadget>
<output>12</output>
<gadget id="calculator">12 / 8</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<result>5/8 = around 0.625</result>


if 20 men can build a wall 66 metres long in 10 days , what length of a similar can be built by 86 men in 8 days ?

Explanation: "if 20 men can build a wall 66 metres long in 10 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 10 * 20 ) = 227.04 mtrs answer : a"

multiply(66, divide(multiply(86, 8), multiply(20, 10)))

<gadget id="calculator">86 * 8</gadget>
<output>688</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">688 / 200</gadget>
<output>86/25 = around 3.44</output>
<gadget id="calculator">66 * (86/25)</gadget>
<output>5_676/25 = around 227.04</output>
<result>5_676/25 = around 227.04</result>


if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 9 ) , what is the value of x ?

Explanation: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 9 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 9 hence x = 11 . answer is b"

<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<result>11</result>


by travelling at 60 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?

Explanation: "let the time taken to reach the destination be 3 x hours . total distance = 60 * 3 x = 180 x km he covered 2 / 3 * 180 x = 120 x km in 1 / 3 * 3 x = x hours so , the remaining 60 x km , he has to cover in 2 x hours . required speed = 60 x / 2 x = 30 kmph . answer : a"

divide(subtract(multiply(60, const_3), divide(multiply(multiply(60, const_3), const_2), const_3)), subtract(const_3, const_1))

<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">180 * 2</gadget>
<output>360</output>
<gadget id="calculator">360 / 3</gadget>
<output>120</output>
<gadget id="calculator">180 - 120</gadget>
<output>60</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>30</result>


a candidate got 35 % of the votes polled and he lost to his rival by 2430 votes . how many votes were cast ?

Explanation: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2430 100 % - - - - - - - - - ? = > 8100 answer : c"

divide(2430, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100)))

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">1 - (7/20)</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">(13/20) - (7/20)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">2_430 / (3/10)</gadget>
<output>8_100</output>
<result>8_100</result>


if the average of 5 positive integers is 65 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 65 = 325 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 325 i . e . 5 a = 315 i . e . a = 63 i . e . largest e = 63 + 10 = 73 answer : option e"

add(divide(subtract(multiply(65, 5), 10), 5), 10)

<gadget id="calculator">65 * 5</gadget>
<output>325</output>
<gadget id="calculator">325 - 10</gadget>
<output>315</output>
<gadget id="calculator">315 / 5</gadget>
<output>63</output>
<gadget id="calculator">63 + 10</gadget>
<output>73</output>
<result>73</result>


p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 20 days to complete the same work . then q alone can do it in

Explanation: "work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 20 work done by p , q and r in 1 day = 1 / 10 + 1 / 20 = 3 / 20 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 3 / 20 = > work done by p in 1 day = 3 / 40 = > work done by q and r in 1 day = 3 / 40 hence work done by q in 1 day = 3 / 40 â € “ 1 / 20 = 1 / 40 so q alone can do the work in 40 days answer is e ."

divide(const_1, subtract(divide(add(divide(const_1, 10), divide(const_1, 20)), const_2), divide(const_1, 20)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) / 2</gadget>
<output>3/40 = around 0.075</output>
<gadget id="calculator">(3/40) - (1/20)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>40</result>


sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6500 ?

Explanation: total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 34009 ) = rs . 4966 answer : a

<gadget id="calculator">6_835 + 9_927</gadget>
<output>16_762</output>
<gadget id="calculator">16_762 + 6_855</gadget>
<output>23_617</output>
<gadget id="calculator">23_617 + 7_230</gadget>
<output>30_847</output>
<gadget id="calculator">30_847 + 6_562</gadget>
<output>37_409</output>
<gadget id="calculator">37_409 / 5</gadget>
<output>37_409/5 = around 7_481.8</output>
<gadget id="calculator">(37_409/5) - 6_500</gadget>
<output>4_909/5 = around 981.8</output>
<gadget id="calculator">(4_909/5) * 5</gadget>
<output>4_909</output>
<result>4_909</result>


find the area of a parallelogram with base 15 cm and height 40 cm ?

Explanation: "area of a parallelogram = base * height = 15 * 40 = 600 cm 2 answer : d"

<gadget id="calculator">15 * 40</gadget>
<output>600</output>
<result>600</result>


a sum of money is distributed among a , b , c , d in the proportion of 1 : 3 : 4 : 2 . if c gets $ 500 more than d , what is the b ' s share ?

Explanation: let the shares of a , b , c , d are x , 3 x , 4 x , 2 x 4 x - 2 x = 500 x = 250 b ' s share = 3 x = $ 750 answer is c

divide(multiply(divide(multiply(add(500, 500), 2), 4), 3), 2)

<gadget id="calculator">500 + 500</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 2</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 4</gadget>
<output>500</output>
<gadget id="calculator">500 * 3</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 2</gadget>
<output>750</output>
<result>750</result>


the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 507 sq m , then what is the breadth of the rectangular plot ?

Explanation: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 507 3 b 2 = 507 b 2 = 169 b = 13 m . answer : option c"

<gadget id="calculator">507 / 3</gadget>
<output>169</output>
<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>
<result>13</result>


the number 341 is equal to the sum of the cubes of two integers . what is the product of those integers ?

Explanation: 5 ^ 3 + 6 ^ 3 = 341 number is 5 * 6 = 30 d

multiply(floor(power(divide(341, const_2), divide(const_1, const_3))), power(subtract(341, power(floor(power(divide(341, const_2), divide(const_1, const_3))), const_3)), divide(const_1, const_3)))

<gadget id="calculator">341 / 2</gadget>
<output>341/2 = around 170.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(341/2) ** (1/3)</gadget>
<output>2**(2/3)*341**(1/3)/2 = around 5.545084</output>
<gadget id="calculator">floor(2**(2/3)*341**(1/3)/2)</gadget>
<output>5</output>
<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">341 - 125</gadget>
<output>216</output>
<gadget id="calculator">216 ** (1/3)</gadget>
<output>6</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<result>30</result>


Explanation: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 25 x 9 ) / 45 = 5 correct option : c"

divide(multiply(divide(25, const_100), 900), 45)

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 900</gadget>
<output>225</output>
<gadget id="calculator">225 / 45</gadget>
<output>5</output>
<result>5</result>


| x + 3 | – | 4 - x | = | 7 + x | how many solutions will this equation have ?

Explanation: you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , s ố x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , s ố í t becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 c

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">14 / 7</gadget>
<output>2</output>
<result>2</result>


a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is

Explanation: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 3 = 2 ( x + 3 ) â € ¹ = â € º x + 27 = 2 x + 6 x = 21 . answer d"

divide(subtract(24, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">24 - 2</gadget>
<output>22</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">22 / 1</gadget>
<output>22</output>
<result>22</result>


a man covers a certain distance q in a train . if the train moved 4 km / hr faster , it would take 30 min less . if it moved 2 km / hr slower , it would take 20 mins more . find the distance ?

Explanation: not really . when you solve the 2 equation above , you get , 6 t - 4 / 3 = 5 r / 6 from simplifying equation 1 4 t - 2 = r / 2 from simplifying equation 2 you can now multiply equation 2 by 5 to get 5 ( 4 t - 2 = r / 2 ) = 20 t - 10 = 5 r / 2 and then subtract this new equation from equation 1 to get t = 3 , followed by r = 20 to give you distance q = r * t = 20 * 3 = 60 km . d

multiply(divide(subtract(multiply(4, 2), 4), const_2), 30)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 - 4</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">2 * 30</gadget>
<output>60</output>
<result>60</result>


if the a radio is sold for rs 490 and sold for rs 465.50 . find loss % .

Explanation: "sol . cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . loss % = [ ( 24.50 / 490 ) * 100 ] % = 5 % answer is b ."

multiply(divide(subtract(490, 465.50), 490), const_100)

<gadget id="calculator">490 - 465.5</gadget>
<output>24.5</output>
<gadget id="calculator">24.5 / 490</gadget>
<output>0.05</output>
<gadget id="calculator">0.05 * 100</gadget>
<output>5</output>
<result>5</result>


a cycle is bought for rs . 900 and sold for rs . 1160 , find the gain percent ?

Explanation: "900 - - - - 260 100 - - - - ? = > 29 % answer : b"

multiply(divide(subtract(1160, 900), 900), const_100)

<gadget id="calculator">1_160 - 900</gadget>
<output>260</output>
<gadget id="calculator">260 / 900</gadget>
<output>13/45 = around 0.288889</output>
<gadget id="calculator">(13/45) * 100</gadget>
<output>260/9 = around 28.888889</output>
<result>260/9 = around 28.888889</result>


the perimeter of a rectangular yard is completely surrounded by a fence that measures 12 meters . what is the length of the yard if the area of the yard is 9 meters squared ?

Explanation: perimeter of rectangular yard = 2 ( l + b ) = 12 - - > l + b = 6 area = l * b = 9 b = 6 - l l ( 6 - l ) = 9 6 l - l ^ 2 = 9 l ^ 2 - 6 l + 9 = 0 upon simplifying we get l = 3 . answer : b

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


x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 7 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 / 7 ^ 2 = 9 / 49 answer : e

divide(multiply(1, power(3, const_2)), power(7, const_2))

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1 * 9</gadget>
<output>9</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">9 / 49</gadget>
<output>9/49 = around 0.183673</output>
<result>9/49 = around 0.183673</result>


a rectangular wall is covered entirely with two kinds of decorative tiles : regular and jumbo . 1 / 3 of the tiles are jumbo tiles , which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles . if regular tiles cover 50 square feet of the wall , and no tiles overlap , what is the area of the entire wall ?

Explanation: "the number of jumbo tiles = x . the number of regular tiles = 2 x . assume the ratio of the dimensions of a regular tile is a : a - - > area = a ^ 2 . the dimensions of a jumbo tile is 3 a : 3 a - - > area = 9 a ^ 2 . the area of regular tiles = 2 x * a ^ 2 = 50 . the area of jumbo tiles = x * 9 a ^ 2 = 4.5 ( 2 x * a ^ 2 ) = 4.5 * 50 = 225 . total area = 50 + 225 = 275 . answer : b ."

add(50, multiply(divide(multiply(50, 3), const_2), 3))

<gadget id="calculator">50 * 3</gadget>
<output>150</output>
<gadget id="calculator">150 / 2</gadget>
<output>75</output>
<gadget id="calculator">75 * 3</gadget>
<output>225</output>
<gadget id="calculator">50 + 225</gadget>
<output>275</output>
<result>275</result>


a clothing store purchased a pair of pants for $ 90 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a clothing store owner decided to decrease the selling price by 20 percent . what was the clothing store ' s gross profit on this sale ?

Explanation: sale price ( sp ) = 90 + markup ( mp ) - - > mp = sp - 90 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 90 3 sp / 4 = 90 sp = 120 now a discount of 20 % is given so new sp is . 8 * 120 = 96 profit = 96 - 90 = 6.0 $ answer is d

subtract(divide(multiply(subtract(const_100, 20), add(divide(90, const_3), 90)), const_100), 90)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">30 + 90</gadget>
<output>120</output>
<gadget id="calculator">80 * 120</gadget>
<output>9_600</output>
<gadget id="calculator">9_600 / 100</gadget>
<output>96</output>
<gadget id="calculator">96 - 90</gadget>
<output>6</output>
<result>6</result>


the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 6 per metre approximately

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 6 ) = rs . 8915 . answer : option e"

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 6)


the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q 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>


a is twice as good a workman as b and they took 8 days together to do the work b alone can do it in .

Explanation: "wc = 2 : 1 2 x + x = 1 / 8 x = 1 / 24 = > 24 days answer : a"

multiply(divide(multiply(8, add(const_2, const_1)), const_2), const_2)

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>24</result>


how many unique positive odd integers less than 70 are equal to the product of a positive multiple of 5 and an odd number ?

Explanation: "the question basically asks how many positive odd integers less than 70 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 and 65 = 7 ans b"

<gadget id="calculator">70 / 5</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>


Explanation: "201834 x 99999 = 201834 x ( 100000 - 1 ) = 201834 x 100000 - 201834 x 1 = 20183400000 - 201834 = 20183198166 a"


if a 5 percent deposit that has been paid toward the purchase of a certain product is $ 70 , how much more remains to be paid ?

Explanation: "95 % remains to be paid so the remaining amount is 19 * 70 = $ 1330 . the answer is d ."

subtract(multiply(70, divide(const_100, 5)), 70)

<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">70 * 20</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 - 70</gadget>
<output>1_330</output>
<result>1_330</result>


for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?

Explanation: concept : when terms are in arithmetic progression ( a . p . ) i . e . terms are equally spaced then mean = median = ( first + last ) / 2 and sum = mean * number of terms h ( 18 ) = [ ( 4 + 18 ) / 2 ] * 8 = 88 h ( 10 ) = ( 4 + 10 ) / 2 ] * 4 = 28 h ( 18 ) / h ( 10 ) = ( 88 ) / ( 28 ) ~ 3 answer : a

divide(divide(multiply(add(18, 4), add(divide(subtract(18, 4), const_2), const_1)), const_2), divide(multiply(add(divide(subtract(10, 4), const_2), const_1), add(4, 10)), const_2))

<gadget id="calculator">18 + 4</gadget>
<output>22</output>
<gadget id="calculator">18 - 4</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">22 * 8</gadget>
<output>176</output>
<gadget id="calculator">176 / 2</gadget>
<output>88</output>
<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 + 10</gadget>
<output>14</output>
<gadget id="calculator">4 * 14</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">88 / 28</gadget>
<output>22/7 = around 3.142857</output>
<result>22/7 = around 3.142857</result>


sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1.5 % more . she would get how much ?

Explanation: ( 8000 * 3 * 1.5 ) / 100 = 360 9200 - - - - - - - - 9560 answer : a

add(multiply(multiply(add(divide(1.5, const_100), divide(divide(subtract(9200, 8000), 3), 8000)), 8000), 3), 8000)

<gadget id="calculator">1.5 / 100</gadget>
<output>0.015</output>
<gadget id="calculator">9_200 - 8_000</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 / 3</gadget>
<output>400</output>
<gadget id="calculator">400 / 8_000</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">0.015 + (1/20)</gadget>
<output>0.065</output>
<gadget id="calculator">0.065 * 8_000</gadget>
<output>520</output>
<gadget id="calculator">520 * 3</gadget>
<output>1_560</output>
<gadget id="calculator">1_560 + 8_000</gadget>
<output>9_560</output>
<result>9_560</result>


a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 12 m long . over how much area of the field can it graze ?

Explanation: "area of the shaded portion = 1 ⁄ 4 × π × ( 12 ) 2 = 113 m 2 answer b"

divide(multiply(power(12, const_2), const_pi), const_4)

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">144 * pi</gadget>
<output>144*pi = around 452.389342</output>
<gadget id="calculator">(144*pi) / 4</gadget>
<output>36*pi = around 113.097336</output>
<result>36*pi = around 113.097336</result>


there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

Explanation: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 170 ) = 1057 - 1020 = 37 . answer a"

subtract(multiply(151, 7), multiply(6, 170))

<gadget id="calculator">151 * 7</gadget>
<output>1_057</output>
<gadget id="calculator">6 * 170</gadget>
<output>1_020</output>
<gadget id="calculator">1_057 - 1_020</gadget>
<output>37</output>
<result>37</result>


the mean of 50 observations is 100 . but later he found that there is decrements of 13 from each observations . what is the the updated mean is ?

Explanation: "87 answer is a"

<gadget id="calculator">100 - 13</gadget>
<output>87</output>
<result>87</result>


a pupil ' s marks were wrongly entered as 83 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 83 - 63 ) = > x / 2 = 20 = > x = 40 answer : c"

<gadget id="calculator">83 - 63</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<result>40</result>


a trader sells 23 meters of cloth for rs . 529 at the profit of rs . 5 per metre of cloth . what is the cost price of one metre of cloth ?

Explanation: "sp of 1 m of cloth = 529 / 23 = rs . 23 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 23 - rs . 5 = rs . 18 answer : e"

<gadget id="calculator">529 / 23</gadget>
<output>23</output>
<gadget id="calculator">23 - 5</gadget>
<output>18</output>
<result>18</result>


if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 54 more . what is the cost price ?

Explanation: 9 % * cost price = $ 54 1 % * cost price = $ 54 / 9 = $ 6 the cost price is $ 600 . the answer is b .

<gadget id="calculator">54 / 9</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<result>600</result>


if 8 cats can kill 8 rats in 8 minutes , how long will it take 100 cats to kill 100 rats ?

Explanation: it will take 8 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 8 minutes , so 100 cats can kill 100 rats in 8 minutes answer c

<gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>8</result>


peter invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 600 at the end of another 2 years . what was the rate of interest in which he invested his sum ?

Explanation: "lets assume the principal amount ( initial amount invested ) to be p rate of interest to berand time as t . we need to find r now after a time of 3 years the principal p amounts to $ 400 and after a time of 5 years ( question says after another 5 years so 3 + 2 ) p becomes $ 600 . formulating the above data amount ( a 1 ) at end of 3 years a 1 = p ( 1 + 3 r / 100 ) = 400 amount ( a 2 ) at end of 8 years a 2 = p ( 1 + 5 r / 100 ) = 600 dividing a 2 by a 1 we get ( 1 + 5 r / 100 ) / ( 1 + 3 r / 100 ) = 6 / 8 after cross multiplication we are left with r = 100 option : a"

multiply(divide(divide(subtract(600, 400), 2), subtract(400, multiply(divide(subtract(600, 400), 2), 3))), const_100)

<gadget id="calculator">600 - 400</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">100 * 3</gadget>
<output>300</output>
<gadget id="calculator">400 - 300</gadget>
<output>100</output>
<gadget id="calculator">100 / 100</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>100</result>


Explanation: "e 762 ? = 5080 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 762"

multiply(multiply(multiply(divide(3, 4), divide(1, 2)), divide(2, 5)), 5080)

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(3/4) * (1/2)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/8) * (2/5)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 5_080</gadget>
<output>762</output>
<result>762</result>


Explanation: √ 4 = 2 so , √ 4 percent of 4 √ 4 = 2 percent of ( 4 ) ( 2 ) = ( 2 / 100 ) ( 8 ) = 16 / 100 = 0.16 answer : a

divide(multiply(multiply(sqrt(4), sqrt(4)), 4), const_100)

<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<result>4/25 = around 0.16</result>


12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 12 hours a day , the number of men required ?

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 12 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 12 × 8 = 8 days e )"

divide(multiply(multiply(12, 10), 8), multiply(8, 12))

<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<gadget id="calculator">120 * 8</gadget>
<output>960</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">960 / 96</gadget>
<output>10</output>
<result>10</result>


8 people decided to split the restaurant bill evenly . if the bill was $ 214.15 dollars , how much money did they 1 cent is the smallest unit ?

Explanation: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 415 not divisible by a hence , we need to add 1 to this number for it to be divisible by 8 correct option : a"

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">214.15 + (3/100)</gadget>
<output>214.18</output>
<result>214.18</result>


a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what y percent of the list price is the lowest possible sale price ?

Explanation: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which y is 40 % of 80 hence , d is the answer"

<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>


each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 12500 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period .

Explanation: "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate a , b , d , e the answer to be c again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 5120 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 5120 = 12500 hence , correct answer = c"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) ** 4</gadget>
<output>625/256 = around 2.441406</output>
<gadget id="calculator">12_500 / (625/256)</gadget>
<output>5_120</output>
<result>5_120</result>


a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000.00001 more . at the end of the year , their profits amounted to rs . 714 find the share of a .

Explanation: explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 714 = 272 answer : b

multiply(divide(714, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>
<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>
<gadget id="calculator">714 / 84_000</gadget>
<output>17/2_000 = around 0.0085</output>
<gadget id="calculator">(17/2_000) * 32_000</gadget>
<output>272</output>
<result>272</result>


a train 120 m long running at 60 kmph crosses a platform in 35 sec . what is the length of the platform ?

Explanation: "d = 60 * 5 / 18 = 35 = 583 – 120 = 463 answer : c"

subtract(multiply(35, multiply(60, const_0_2778)), 120)

<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">35 * (50/3)</gadget>
<output>1_750/3 = around 583.333333</output>
<gadget id="calculator">(1_750/3) - 120</gadget>
<output>1_390/3 = around 463.333333</output>
<result>1_390/3 = around 463.333333</result>


jar a has 6 % more marbles than jar b . what percent of marbles from jar a need to be moved into jar b so that both jars have equal marbles ?

Explanation: "an easy way to solve this question is by number plugging . assume there are 100 marbles in jar b then in jar a there will be 106 marbles . now , for both jars to have equal marbles we should move 3 marbles from a to b , which is 3 / 106 = ~ 2.8 % of a . answer : a ."

multiply(divide(divide(6, const_2), add(6, const_100)), const_100)

<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">6 + 100</gadget>
<output>106</output>
<gadget id="calculator">3 / 106</gadget>
<output>3/106 = around 0.028302</output>
<gadget id="calculator">(3/106) * 100</gadget>
<output>150/53 = around 2.830189</output>
<result>150/53 = around 2.830189</result>


what number has a 5 : 1 ratio to the number 10 ?

Explanation: "answer : option b explanation : 5 : 1 = x : 10 x = 50 answer : option b"

<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<result>50</result>


a , b and c can do a piece of work in 7 days , 14 days and 28 days respectively . how long will they take to finish the work , if all the three work together ?

Explanation: "1 / 7 + 1 / 14 + 1 / 28 = 7 / 28 = 1 / 4 all three can finish the work in 4 days answer : a"

<gadget id="calculator">1 / 28</gadget>
<output>1/28 = around 0.035714</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / 14</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/7) + (1/14)</gadget>
<output>3/14 = around 0.214286</output>
<gadget id="calculator">(1/28) + (3/14)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / (1/4)</gadget>
<output>4</output>
<result>4</result>


in the youth summer village there are 200 people , 100 of them are not working , 75 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?

Explanation: total = 200 not working = 100 having family = 75 like to sing in shower = 125 working = 200 - 100 = 100 not having family = 200 - 75 = 125 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 c

<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">175 + 125</gadget>
<output>300</output>
<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<result>100</result>


nitin ranks 18 th in a class of 49 students . what is rank from the last ?

Explanation: "explanation : number students behind the nitin in rank = ( 49 - 18 ) = 31 nitin is 32 nd from the last answer : c ) 32"

<gadget id="calculator">49 - 18</gadget>
<output>31</output>
<result>31</result>


lamp a flashes every 6 seconds , lamp b flashes every 8 seconds , lamp c flashes every 10 seconds . at a certain instant of time all 3 lamps flash simultaneously . during the period of 6 minutes after that how many times will exactly two lamps flash ? ( please include any flash of exactly two lights which occurs at the 6 minute mark . )

Explanation: 6 minutes is 360 seconds . lamp a and lamp b will flash together every 24 seconds . 360 / 24 = 15 . in the time period , lamp a and lamp b will flash together 15 times . lamp a and lamp c will flash together every 30 seconds . 360 / 30 = 12 . in the time period , lamp a and lamp c will flash together 12 times . lamp b and lamp c will flash together every 40 seconds . 360 / 40 = 9 . in the time period , lamp b and lamp c will flash together 9 times . all three lights will flash together every 2 * 2 * 2 * 3 * 5 = 120 seconds . 360 / 120 = 3 . we have counted these triple flashes three times , so we need to subtract three times the number of times that all three lights flash together . the number of times that exactly two lights flash together is 15 + 12 + 9 - 9 = 27 times . the answer is d .

subtract(add(add(divide(multiply(6, const_60), lcm(6, 8)), divide(multiply(6, const_60), lcm(6, 10))), divide(multiply(6, const_60), lcm(8, 10))), multiply(divide(multiply(6, const_60), lcm(lcm(6, 8), 10)), 3))

<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<gadget id="calculator">lcm(6, 8)</gadget>
<output>24</output>
<gadget id="calculator">360 / 24</gadget>
<output>15</output>
<gadget id="calculator">lcm(6, 10)</gadget>
<output>30</output>
<gadget id="calculator">360 / 30</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">lcm(8, 10)</gadget>
<output>40</output>
<gadget id="calculator">360 / 40</gadget>
<output>9</output>
<gadget id="calculator">27 + 9</gadget>
<output>36</output>
<gadget id="calculator">lcm(24, 10)</gadget>
<output>120</output>
<gadget id="calculator">360 / 120</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">36 - 9</gadget>
<output>27</output>
<result>27</result>


a man walking at a rate of 10 km / hr crosses a bridge in 12 minutes . the length of the bridge is ?

Explanation: speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 10 minutes = 50 / 18 * 12 * 60 = 2000 m answer is a

multiply(divide(multiply(10, const_1000), const_60), 12)

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 60</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">(500/3) * 12</gadget>
<output>2_000</output>
<result>2_000</result>


there are 1000 students in a school and among them 30 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

Explanation: 30 % of 1000 gives 300 . so 300 attends chess and 10 % of 300 gives 30 . so 30 enrolled for swimming answer : d

divide(multiply(divide(multiply(30, 1000), const_100), 10), const_100)

<gadget id="calculator">30 * 1_000</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 100</gadget>
<output>300</output>
<gadget id="calculator">300 * 10</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<result>30</result>


exactly 15 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?

Explanation: "let ' s assume there are 100 reporters - - > 15 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 15 ( # of reporters who cover local politics ) : 0.75 x = 15 - - > x = 20 , hence 20 reporters cover politics and the rest 100 - 20 = 80 reporters do not cover politics at all . answer : d ."

multiply(subtract(const_1, divide(15, subtract(const_100, 25))), const_100)

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">15 / 75</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


of 70 players on a football team , 43 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?

Explanation: "total = 70 thrower = 43 rest = 70 - 43 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 43 + 18 = 61 so c . 61 is the right answer"

add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 43)), 43)

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">70 - 43</gadget>
<output>27</output>
<gadget id="calculator">(2/3) * 27</gadget>
<output>18</output>
<gadget id="calculator">18 + 43</gadget>
<output>61</output>
<result>61</result>


in how many seconds will a train 100 meters long pass an oak tree , if the speed of the train is 36 km / hr ?

Explanation: "speed = 36 * 5 / 18 = 10 m / s time = 100 / 10 = 10 seconds the answer is c ."

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 36</gadget>
<output>10</output>
<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<result>10</result>


the bus fare for two persons for travelling between agra and aligarh id 4 - thirds the train fare between the same places for one person . the total fare paid by 6 persons travelling by bus and 8 persons travelling by train between the two places is rs . 1512 . find the train fare between the two places for one person ?

Explanation: let the train fare between the two places for one person be rs . t bus fare between the two places for two persons rs . 4 / 3 t = > 6 / 2 ( 4 / 3 t ) + 8 ( t ) = 1512 = > 12 t = 1512 = > t = 126 . answer : a

divide(1512, add(multiply(divide(6, const_2), divide(4, const_3)), 8))

<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 * (4/3)</gadget>
<output>4</output>
<gadget id="calculator">4 + 8</gadget>
<output>12</output>
<gadget id="calculator">1_512 / 12</gadget>
<output>126</output>
<result>126</result>


a goods bullet train runs at the speed of 72 km / hr and crosses a 250 m long platform in 26 seconds . what is the length of the goods bullet train ?

Explanation: e 270 m

subtract(multiply(multiply(72, const_0_2778), 26), 250)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">20 * 26</gadget>
<output>520</output>
<gadget id="calculator">520 - 250</gadget>
<output>270</output>
<result>270</result>


a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?

Explanation: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 10 % of 140 = rs . 140 - 14 = rs . 126 . gain = rs . 126 â € “ rs . 100 = rs . 26 therefore , gain / profit percent = 26 % . answer : option a"

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

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">140 * (1/10)</gadget>
<output>14</output>
<gadget id="calculator">140 - 14</gadget>
<output>126</output>
<gadget id="calculator">126 - 100</gadget>
<output>26</output>
<result>26</result>


Explanation: "according to order of operations , inner brackets first . hence | 6 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 6 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 6 + 72 | - | 5 - 11 | = | 78 | - | - 6 | = 78 - 6 = 72 correct answer c ) 72"

subtract(subtract(6, multiply(8, subtract(3, 12))), negate(subtract(5, 11)))

<gadget id="calculator">3 - 12</gadget>
<output>-9</output>
<gadget id="calculator">8 * (-9)</gadget>
<output>-72</output>
<gadget id="calculator">6 - (-72)</gadget>
<output>78</output>
<gadget id="calculator">5 - 11</gadget>
<output>-6</output>
<gadget id="calculator">-(-6)</gadget>
<output>6</output>
<gadget id="calculator">78 - 6</gadget>
<output>72</output>
<result>72</result>


on a trip , a cyclist averaged 11 miles per hour for the first 22 miles and 10 miles per hour for the remaining 20 miles . if the cyclist returned immediately via the same route and took a total of 9 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?

Explanation: the time to go 42 miles was 22 / 11 + 20 / 10 = 2 + 2 = 4 hours . the average speed for the return trip was 42 miles / 5 hours = 8.4 mph . the answer is e .

divide(add(22, 20), subtract(9, add(divide(22, 11), divide(20, 10))))

<gadget id="calculator">22 + 20</gadget>
<output>42</output>
<gadget id="calculator">22 / 11</gadget>
<output>2</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">9 - 4</gadget>
<output>5</output>
<gadget id="calculator">42 / 5</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>


on increasing the number of lines in a page by 100 , they become 240 . what is the % of increase in the no . of lines in the page ?

Explanation: "explanation : number of pages increased = 100 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 100 = 140 % increase in the number of pages in the book = 100 / 140 x 100 % = 71.4 % d"

subtract(multiply(divide(240, subtract(240, 100)), const_100), const_100)

<gadget id="calculator">240 - 100</gadget>
<output>140</output>
<gadget id="calculator">240 / 140</gadget>
<output>12/7 = around 1.714286</output>
<gadget id="calculator">(12/7) * 100</gadget>
<output>1_200/7 = around 171.428571</output>
<gadget id="calculator">(1_200/7) - 100</gadget>
<output>500/7 = around 71.428571</output>
<result>500/7 = around 71.428571</result>


find the sum 3 / 10 + 5 / 100 + 8 / 1000 in decimal form ?

Explanation: answer 3 / 10 + 5 / 100 + 8 / 1000 = 0.3 + 0.05 + 0.008 = 0.358 correct option : b

<gadget id="calculator">8 / 1_000</gadget>
<output>1/125 = around 0.008</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(3/10) + (1/20)</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(1/125) + (7/20)</gadget>
<output>179/500 = around 0.358</output>
<result>179/500 = around 0.358</result>


3 distinct single digit no a , b , c are in g . p . if abs ( x ) for real x is the absolute value of x ( x if x is positive or zero , and x if x is negative ) , then the no . of different possible values of abs ( a + b - c ) is

Explanation: if a = 1 , r = 2 then a = 1 , b = 2 , c = 4 then abs ( a + b - c ) = 1 if a = 1 , r = 3 then a = 1 , a = 3 , a = 9 then abs ( 1 + 3 - 9 ) = 5 if a = 2 , r = 2 , then a = 2 , b = 4 , c = 8 then abs ( 2 + 4 - 8 ) = 2 if a = 1 , r = - 2 then a = 1 , b = - 2 , c = 4 the abs ( 1 - 2 - 4 ) = 5 if a = 1 , r = - 3 then a = 1 , b = - 3 , c = 9 then abs ( 1 - 3 - 9 ) = 11 if a = 2 , r = - 2 then a = 2 , b = - 4 , c = - 8 then abs ( 2 - 4 - 8 ) = 10 so total 5 abs ( ) values answer : d

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<result>5</result>


Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 19 odd numbers = 19 ^ 2 = 361 answer : c"

multiply(multiply(19, const_2), divide(19, const_2))

<gadget id="calculator">19 * 2</gadget>
<output>38</output>
<gadget id="calculator">19 / 2</gadget>
<output>19/2 = around 9.5</output>
<gadget id="calculator">38 * (19/2)</gadget>
<output>361</output>
<result>361</result>


an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 25 coaches are attached .

Explanation: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 25 swr root = 5 decrease = 5 * 4 = 20 new speed = 90 - 20 = 70 e"

subtract(90, multiply(sqrt(25), divide(subtract(90, 78), sqrt(9))))

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">90 - 78</gadget>
<output>12</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">90 - 20</gadget>
<output>70</output>
<result>70</result>


a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 264 metres long in 20 seconds . the length of the train ( in metres ) is :

Explanation: "explanation : let the length of train be l m . acc . to question ( 264 + l ) / 20 = l / 8 2112 + 8 l = 20 l l = 2112 / 12 = 176 m answer b"

multiply(divide(264, subtract(20, 8)), 8)

<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">264 / 12</gadget>
<output>22</output>
<gadget id="calculator">22 * 8</gadget>
<output>176</output>
<result>176</result>


a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 10 miles per gallon , and from town b to town c , the car averaged 12 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?

Explanation: "step 1 ) took lcm of 10 and 12 . . came as 30 . just multiplied by 10 . . . ( to make easy calculation ) step 2 ) 300 distance between b to c . . . do 300 / 12 hence 25 gallons used step 3 ) twice distance . . hence 300 * 2 = 600 . . . do as above . . 600 / 10 = 60 gallons used step 4 ) total gallons . . 25 + 60 = 85 gallons step ) total miles = 300 + 600 = 900 miles hence . . average of whole journey = 900 / 85 which comes to 10.6 answer : d"

divide(add(multiply(12, const_10), divide(multiply(12, const_10), const_2)), add(divide(multiply(12, const_10), 10), divide(divide(multiply(12, const_10), const_2), 12)))

<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">120 + 60</gadget>
<output>180</output>
<gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">60 / 12</gadget>
<output>5</output>
<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">180 / 17</gadget>
<output>180/17 = around 10.588235</output>
<result>180/17 = around 10.588235</result>


on sunday , bill ran 4 more miles than he ran on saturday . julia did not run on saturday , but she ran twice the number of miles on sunday that bill ran on sunday . if bill and julia ran a total of 16 miles on saturday and sunday , how many miles did bill run on sunday ?

Explanation: "let bill run x on saturday , so he will run x + 4 on sunday . . julia will run 2 * ( x + 4 ) on sunday . . totai = x + x + 4 + 2 x + 8 = 16 . . 4 x + 12 = 16 . . x = 1 . . ans = x + 4 = 1 + 4 = 5 answer a"

add(divide(subtract(16, add(4, multiply(const_2, 4))), 4), 4)

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">4 + 8</gadget>
<output>12</output>
<gadget id="calculator">16 - 12</gadget>
<output>4</output>
<gadget id="calculator">4 / 4</gadget>
<output>1</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<result>5</result>


a train 450 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?

Explanation: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 450 m at 50 / 3 m / sec = 450 * 3 / 50 sec = 27 sec answer : c ."

divide(450, multiply(subtract(68, 8), const_0_2778))

<gadget id="calculator">68 - 8</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">450 / (50/3)</gadget>
<output>27</output>
<result>27</result>


during a thanksgiving weekend , a car rental company rented 6 - tenths of their vehicles , including two - fifths of the 4 wds that it had . if 40 % of the vehicles are 4 wds , then what percent of the vehicles that were not rented were not 4 wds ?

Explanation: 4 / 10 of all the vehicles were not rented . ( 3 / 5 ) ( 2 / 5 ) = 6 / 25 of all the vehicles are 4 wds that were not rented . ( 6 / 25 ) / ( 4 / 10 ) = 3 / 5 is the fraction of non - rented vehicles that were 4 wds 1 - 3 / 5 = 40 % of non - rented vehicles were not 4 wds . the answer is c .

multiply(divide(divide(multiply(const_2, 40), add(const_3, const_2)), 40), const_100)

<gadget id="calculator">2 * 40</gadget>
<output>80</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<gadget id="calculator">16 / 40</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>


if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?

Explanation: "we have : 1 ) x < y < z 2 ) y - x > 5 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we can eliminate answer choices a , c and e we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 7 the least value for y - x must be 11 , the least value for x must be 2 , and , thus , the least possible value for y must be 11 ( y - 2 = 9 , y = 11 ) 2 < 11 < z , since z is odd , the least possible value for z is 13 z - x = 13 - 2 = 11 answer c"

<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<result>11</result>


jim drove 1096 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?

Explanation: "the number of miles to drive to finish his journey is given by 1200 - 1096 = 104 miles correct answer a"

<gadget id="calculator">1_200 - 1_096</gadget>
<output>104</output>
<result>104</result>


ram , who is half as efficient as krish , will take 18 days to complete a task if he worked alone . if ram and krish worked together , how long will they take to complete the task ?

Explanation: "number of days taken by ram to complete task = 18 since ram is half as efficient as krish , amount of work done by krish in 1 day = amount of work done by ram in 2 days if total work done by ram in 18 days is 18 w amount of work done by ram in 1 day = w amount of work done by krish in 1 day = 2 w total amount of work done by krish and ram in a day = 3 w total amount of time needed by krish and ram to complete task = 18 w / 3 w = 6 days answer d"

inverse(add(divide(const_1, 18), divide(const_1, divide(18, const_2))))

<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/18) + (1/9)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / (1/6)</gadget>
<output>6</output>
<result>6</result>


a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :

Explanation: "external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 x [ ( 4 ) ^ 2 - ( 3 ) ^ 2 ] x 21 ) cm ^ 3 ( 22 / 7 x 7 x 1 x 21 ) cm ^ 3 462 cm ^ 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), 1), 21)), 8), const_1000)

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">pi * (4 ** 2) * 21</gadget>
<output>336*pi = around 1_055.575132</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">pi * (3 ** 2) * 21</gadget>
<output>189*pi = around 593.761012</output>
<gadget id="calculator">(336*pi) - (189*pi)</gadget>
<output>147*pi = around 461.81412</output>
<gadget id="calculator">(147*pi) * 8</gadget>
<output>1176*pi = around 3_694.512961</output>
<gadget id="calculator">(1176*pi) / 1_000</gadget>
<output>147*pi/125 = around 3.694513</output>
<result>147*pi/125 = around 3.694513</result>


the average weight of 7 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?

Explanation: "total weight increases = 7 × 1.5 = 10.5 kg so the weight of new person = 65 + 10.5 = 75.5 kg answer c"

<gadget id="calculator">7 * 1.5</gadget>
<output>10.5</output>
<gadget id="calculator">65 + 10.5</gadget>
<output>75.5</output>
<result>75.5</result>


mr . jones gave 40 % of the money he had to his wife . he also gave 20 % of the remaining amount to his 3 sons . and half of the amount now left was spent on miscellaneous items and the remaining amount of rs . 12000 was deposited in the bank . how much money did mr . jones have initially ?

Explanation: explanation : let the initial amount be x , amount given to his wife = ( 40 / 100 ) x = 2 x / 5 balance = ( x - ( 2 x / 5 ) ) = 3 x / 5 amount given to his wife = ( 20 / 100 ) * ( 3 x / 5 ) = 3 x / 25 balance = 3 x / 5 - 3 x / 25 = 12 x / 25 amountt spent on miscellaneous items = ( 1 / 2 ) * ( 12 x / 25 ) = 6 x / 25 which is equal to 12000 hence , = > 6 x / 25 = 12000 = > x = 50000 answer : c

divide(12000, multiply(divide(divide(const_100, const_2), const_100), multiply(subtract(const_1, divide(40, const_100)), subtract(const_1, divide(20, const_100)))))

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(3/5) * (4/5)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">(1/2) * (12/25)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">12_000 / (6/25)</gadget>
<output>50_000</output>
<result>50_000</result>


he total marks obtained by a student in physics , chemistry and mathematics is 170 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?

Explanation: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 170 + p c + m = 170 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 170 / 2 = 85 . answer : d"

<gadget id="calculator">170 / 2</gadget>
<output>85</output>
<result>85</result>


25 onions on a scale weigh 5.12 kg . when 3 onions are removed from the scale , the average weight of the 22 onions is 200 grams . what is the average weight ( in grams ) of the 3 onions which were removed ?

Explanation: 22 * 200 = 4400 . the other 3 onions weigh a total of 720 grams . the average weight is 720 / 3 = 240 grams . the answer is c .

divide(subtract(multiply(5.12, const_1000), multiply(22, 200)), 3)

<gadget id="calculator">5.12 * 1_000</gadget>
<output>5_120</output>
<gadget id="calculator">22 * 200</gadget>
<output>4_400</output>
<gadget id="calculator">5_120 - 4_400</gadget>
<output>720</output>
<gadget id="calculator">720 / 3</gadget>
<output>240</output>
<result>240</result>


a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?

Explanation: "a profit of rs . 600 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 360 and 240 . difference in profit share = 360 - 240 = 120 answer : b"

subtract(divide(divide(600, add(divide(1, 2), divide(1, 3))), 2), divide(divide(600, add(divide(1, 2), divide(1, 3))), 3))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">600 / (5/6)</gadget>
<output>720</output>
<gadget id="calculator">720 / 2</gadget>
<output>360</output>
<gadget id="calculator">720 / 3</gadget>
<output>240</output>
<gadget id="calculator">360 - 240</gadget>
<output>120</output>
<result>120</result>


3 candidates contested an election and received 1000 , 2000 and 4000 votes respectively . what percentage of the total votes did the winning candidate got ?

Explanation: total number of votes polled = ( 1000 + 2000 + 4000 ) = 7000 required percentage = 4000 / 7000 * 100 = 57 % ( approximately ) answer : option c

<gadget id="calculator">1_000 + 2_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 + 4_000</gadget>
<output>7_000</output>
<gadget id="calculator">4_000 / 7_000</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">(4/7) * 100</gadget>
<output>400/7 = around 57.142857</output>
<result>400/7 = around 57.142857</result>


an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 64 times the difference between the two numbers . how many coins did the old man have ?

Explanation: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 64 ( x - y ) - - > x + y = 64 . answer : d ."

<gadget id="calculator">floor(64)</gadget>
<output>64</output>
<result>64</result>


20 litres of mixture contains 40 % alcohol and the rest water . if 8 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?

Explanation: "alcohol in the 20 litres of mix . = 40 % of 20 litres = ( 40 * 20 / 100 ) = 8 litres water in it = 20 - 8 = 12 litres new quantity of mix . = 20 + 8 = 28 litres quantity of alcohol in it = 8 litres percentage of alcohol in new mix . = 8 * 100 / 28 = 50 / 3 = 28.57 % answer is c"

multiply(divide(subtract(add(20, 8), add(multiply(divide(subtract(const_100, 40), const_100), 20), 8)), add(20, 8)), const_100)

<gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 20</gadget>
<output>12</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">28 - 20</gadget>
<output>8</output>
<gadget id="calculator">8 / 28</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>


Explanation: "= 12.036 / 0.04 = 1203.6 / 4 = 300.9 answer is b ."

<gadget id="calculator">12.036 / 0.04</gadget>
<output>300.9</output>
<result>300.9</result>


if 20 liters of chemical x are added to 80 liters of a mixture that is 5 % chemical x and 95 % chemical y , then what percentage of the resulting mixture is chemical x ?

Explanation: "the amount of chemical x in the solution is 20 + 0.05 ( 80 ) = 24 liters . 24 liters / 100 liters = 24 % the answer is a ."

add(20, multiply(divide(5, const_100), 80))

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 80</gadget>
<output>4</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<result>24</result>


for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score r for the exam ?

Explanation: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean r = 74 . answer : a ."

divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))

<gadget id="calculator">58 * 3</gadget>
<output>174</output>
<gadget id="calculator">98 * 2</gadget>
<output>196</output>
<gadget id="calculator">174 + 196</gadget>
<output>370</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">370 / 5</gadget>
<output>74</output>
<result>74</result>


a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 240 meter length ?

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 240 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : e"

divide(add(360, 240), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">360 + 240</gadget>
<output>600</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">600 / (25/2)</gadget>
<output>48</output>
<result>48</result>


in one year , the population , of a village increased by 10 % and in the next year , it decreased by 10 % . if at the end of 2 nd year , the population was 7920 , what was it in the beginning ?

Explanation: "x * 110 / 100 * 90 / 100 = 7920 x * 0.99 = 7920 x = 7920 / 0.99 = > 8000 answer : b"

divide(divide(7920, subtract(const_1, divide(10, const_100))), add(const_1, divide(10, const_100)))

<gadget id="calculator">10 / 100</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">7_920 / (9/10)</gadget>
<output>8_800</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">8_800 / (11/10)</gadget>
<output>8_000</output>
<result>8_000</result>


the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 35 % profit ?

Explanation: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 135 % of $ 640 = $ 864 d"

add(divide(multiply(divide(add(832, 448), const_2), 35), const_100), divide(add(832, 448), const_2))

<gadget id="calculator">832 + 448</gadget>
<output>1_280</output>
<gadget id="calculator">1_280 / 2</gadget>
<output>640</output>
<gadget id="calculator">640 * 35</gadget>
<output>22_400</output>
<gadget id="calculator">22_400 / 100</gadget>
<output>224</output>
<gadget id="calculator">224 + 640</gadget>
<output>864</output>
<result>864</result>


if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 3720 , r will receive

Explanation: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 3720 * ( 6 / 31 ) = 120 * 6 = 720 . answer : option a"

multiply(3720, divide(6, add(add(add(10, add(4, const_1)), 10), 6)))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 + 6</gadget>
<output>31</output>
<gadget id="calculator">6 / 31</gadget>
<output>6/31 = around 0.193548</output>
<gadget id="calculator">3_720 * (6/31)</gadget>
<output>720</output>
<result>720</result>


it costs $ 2 for the first 15 minutes to use the bumper cars at a fair ground . after the first 15 minutes it costs $ 6 per hour . if a certain customer uses the bumper cars for 3 hours and 25 minutes , how much will it cost him ?

Explanation: 3 hrs 25 min = 205 min first 15 min - - - - - - > $ 2 time left is 190 min . . . now , 60 min costs $ 6 1 min costs $ 6 / 60 190 min costs $ 6 / 60 * 190 = > $ 19 so , total cost will be $ 19 + $ 2 = > $ 21 the answer will be ( d ) $ 21

add(multiply(divide(6, const_60), subtract(add(multiply(3, const_60), 25), 15)), 2)

<gadget id="calculator">6 / 60</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">180 + 25</gadget>
<output>205</output>
<gadget id="calculator">205 - 15</gadget>
<output>190</output>
<gadget id="calculator">(1/10) * 190</gadget>
<output>19</output>
<gadget id="calculator">19 + 2</gadget>
<output>21</output>
<result>21</result>


a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 30 paise per sq . metre

Explanation: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 30 = 25500 p in rs = 25500 / 100 = rs 255 answer : a"

divide(multiply(subtract(multiply(110, 65), multiply(subtract(110, multiply(2.5, const_2)), subtract(65, multiply(2.5, const_2)))), 30), const_100)

<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>
<gadget id="calculator">2.5 * 2</gadget>
<output>5</output>
<gadget id="calculator">110 - 5</gadget>
<output>105</output>
<gadget id="calculator">65 - 5</gadget>
<output>60</output>
<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>
<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>
<gadget id="calculator">850 * 30</gadget>
<output>25_500</output>
<gadget id="calculator">25_500 / 100</gadget>
<output>255</output>
<result>255</result>


john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?

Explanation: amount of work done by john and andrew in 1 day = 1 / 9 amount of work done by john and andrew in 6 days = 6 ã — ( 1 / 9 ) = 2 / 3 remaining work â € “ 1 â € “ 2 / 3 = 1 / 3 john completes 1 / 3 work in 6 days amount of work john can do in 1 day = ( 1 / 3 ) / 6 = 1 / 18 = > john can complete the work in 18 days answer : c

divide(6, subtract(const_1, divide(6, 9)))

<gadget id="calculator">6 / 9</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">6 / (1/3)</gadget>
<output>18</output>
<result>18</result>


the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 160 runs and his average excluding these two innings is 58 runs , find his highest score .

Explanation: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 160 x + ( x - 160 ) = 208 2 x = 368 x = 184 runs answer : a"

divide(add(160, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>
<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>
<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>
<gadget id="calculator">160 + 208</gadget>
<output>368</output>
<gadget id="calculator">368 / 2</gadget>
<output>184</output>
<result>184</result>


the total age of a and b is 14 years more than the total age of b and c . c is how many year younger than a

Explanation: "explanation : given that a + b = 14 + b + c = > a ? c = 14 + b ? b = 14 = > c is younger than a by 14 years answer : option d"

<gadget id="calculator">14 * 1</gadget>
<output>14</output>
<result>14</result>


if the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m , what is its area ?

Explanation: l - b = 23 . . . ( 1 ) perimeter = 206 2 ( l = b ) = 206 l + b = 103 . . . ( 2 ) ( 1 ) + ( 2 ) 2 l = 23 + 103 = 126 l = 126 / 2 = 63 metre substituting the value of l in ( 1 ) , we get 63 - b = 23 b = 63 - 23 = 40 metre area = lb = 63 ã — 40 = 2520 m 2 answer : a

rectangle_area(add(divide(subtract(206, multiply(const_2, 23)), const_4), 23), divide(subtract(206, multiply(const_2, 23)), const_4))

<gadget id="calculator">2 * 23</gadget>
<output>46</output>
<gadget id="calculator">206 - 46</gadget>
<output>160</output>
<gadget id="calculator">160 / 4</gadget>
<output>40</output>
<gadget id="calculator">40 + 23</gadget>
<output>63</output>
<gadget id="calculator">63 * 40</gadget>
<output>2_520</output>
<result>2_520</result>


a boat having a length 5 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "explanation : volume of water displaced = ( 5 x 2 x 0.01 ) m 3 = 0.10 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.10 x 1000 ) kg = 100 kg . answer : a"

multiply(multiply(multiply(5, 2), divide(1, const_100)), const_1000)

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">10 * (1/100)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 1_000</gadget>
<output>100</output>
<result>100</result>


if 100 cats kill 100 mice in 100 days , then 4 cats would kill 4 mice in how many days ?

Explanation: as 100 cats kill 100 mice in 100 days 1 cats kill 1 mouse in 100 days then 4 cats kill 4 mice in 100 days answer : d

divide(multiply(multiply(4, 100), 100), multiply(100, 4))

<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">400 * 100</gadget>
<output>40_000</output>
<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">40_000 / 400</gadget>
<output>100</output>
<result>100</result>


of the 55 cars on a car lot , 40 have air - conditioning , 25 have power windows , and 12 have both air - conditioning and power windows . how many of the cars on the lot have neither air - conditioning nor power windows ?

Explanation: total - neither = all air conditioning + all power windows - both or 55 - neither = 40 + 25 - 12 = 53 . = > neither = 2 , hence d . answer : d

<gadget id="calculator">40 + 25</gadget>
<output>65</output>
<gadget id="calculator">65 - 12</gadget>
<output>53</output>
<gadget id="calculator">55 - 53</gadget>
<output>2</output>
<result>2</result>


a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 420 less than the sum lent . what was the sum lent ?

Explanation: "p - 420 = ( p * 5 * 8 ) / 100 p = 700 the answer is c ."

divide(420, subtract(const_1, divide(multiply(5, 8), const_100)))

<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">420 / (3/5)</gadget>
<output>700</output>
<result>700</result>


30 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 30 : : 18 : x [ please pay attention , we have written 27 : 30 rather than 30 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 30 \ times 18 } { 27 } } x = 20 so 20 days will be required to get work done by 27 men . answer : a"

<gadget id="calculator">18 * 30</gadget>
<output>540</output>
<gadget id="calculator">540 / 27</gadget>
<output>20</output>
<result>20</result>


if n is a positive integer and n ^ 2 is divisible by 200 , then what is the largest positive integer that must divide n ?

Explanation: 200 = 2 ^ 3 * 5 ^ 2 if 200 divides n ^ 2 , then n must be divisible by 2 ^ 2 * 5 = 20 the answer is c .

<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<result>20</result>


john paid a sum of money for purchasing 20 pens , which he recovered in full when he sold 10 of them . what was his percentage of profit or loss per pen ?

Explanation: a 100 % if the sum he paid whilst purchasing 20 pens = a , then the cost price of each pen = a / 20 . since the amount he got whilst selling 10 pens is also = a then the selling price of each pen = a / 10 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 10 - a / 20 = a / 20 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 20 ) / ( a / 20 ) x 100 = 100 %

multiply(divide(subtract(20, 10), 10), const_100)

<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">10 / 10</gadget>
<output>1</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<result>100</result>


find the smallest number of 6 digits exactly divisible by 25 , 3545 and 15 .

Explanation: smallest number of six digits is 100000 . required number must be divisible by l . c . m . of 25,35 , 45,15 i . e 1575 , on dividing 100000 by 1575 , we get 800 as remainder . therefore , required number = 100000 + ( 1575 â € “ 800 ) = 100775 . answer is b .

<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 10</gadget>
<output>100_000</output>
<result>100_000</result>


in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?

Explanation: ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a

multiply(divide(const_1, add(const_3, const_1)), const_100)

<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


if two - third of a bucket is filled in 6 minute then the time taken to fill the bucket completely will be .

Explanation: "2 / 3 filled in 6 mint 1 / 3 filled in 3 mint thn 2 / 3 + 1 / 3 = 6 + 3 = 9 minutes answer : d"

<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<result>9</result>


a batsman makes a score of 76 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .

Explanation: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 3 ) . ∴ 16 ( x – 3 ) + 76 = 17 x or x = ( 76 – 48 ) = 28 . answer b"

<gadget id="calculator">17 * 3</gadget>
<output>51</output>
<gadget id="calculator">76 - 51</gadget>
<output>25</output>
<gadget id="calculator">25 + 3</gadget>
<output>28</output>
<result>28</result>


find the remainder of the division ( 2 ^ 14 ) / 7 .

Explanation: "find the pattern of the remainders after each power : ( 2 ^ 1 ) / 7 remainder 2 ( 2 ^ 2 ) / 7 remainder 4 ( 2 ^ 3 ) / 7 remainder 1 - - > this is where the cycle ends ( 2 ^ 4 ) / 7 remainder 2 - - > this is where the cycle begins again ( 2 ^ 5 ) / 7 remainder 4 continuing the pattern to ( 2 ^ 14 ) / 7 gives us a remainder of 4 final answer : d ) 4"

<gadget id="calculator">2 ** 14</gadget>
<output>16_384</output>
<gadget id="calculator">16_384 % 7</gadget>
<output>4</output>
<result>4</result>


barbata invests $ 2600 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?

Explanation: "let the additional invested amount for 8 % interest be x ; equation will be ; 2600 + 0.05 * 2600 + x + 0.08 x = 2600 + x + 0.06 ( 2600 + x ) 0.05 * 2600 + 0.08 x = 0.06 x + 0.06 * 2600 0.02 x = 2600 ( 0.06 - 0.05 ) x = 2600 * 0.01 / 0.02 = 1300 ans : ` ` c ' '"

divide(subtract(multiply(divide(6, const_100), 2600), multiply(2600, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100)))

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 2_600</gadget>
<output>156</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">2_600 * (1/20)</gadget>
<output>130</output>
<gadget id="calculator">156 - 130</gadget>
<output>26</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) - (3/50)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">26 / (1/50)</gadget>
<output>1_300</output>
<result>1_300</result>


at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses w at the restaurant ? ( assume that all boxes are filled to capacity . )

Explanation: "most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"

<gadget id="calculator">16 * 2</gadget>
<output>32</output>
<gadget id="calculator">32 * 15</gadget>
<output>480</output>
<result>480</result>


if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?

Explanation: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 40 + ( 11 - 1 ) * 1 } = 11 * 45 = 495 = x number of even number = ( 50 - 40 ) / 2 + 1 = 6 = y x + y = 495 + 6 = 501 d"

add(multiply(divide(add(40, 50), const_2), add(subtract(50, 40), const_1)), add(divide(subtract(50, 40), const_2), const_1))

<gadget id="calculator">40 + 50</gadget>
<output>90</output>
<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">50 - 40</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">45 * 11</gadget>
<output>495</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">495 + 6</gadget>
<output>501</output>
<result>501</result>


a man swims downstream 28 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?

Explanation: "28 - - - 4 ds = 7 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 7 + 4 ) / 2 = 5.5 answer : e"

divide(add(divide(16, 4), divide(28, 4)), const_2)

<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">28 / 4</gadget>
<output>7</output>
<gadget id="calculator">4 + 7</gadget>
<output>11</output>
<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<result>11/2 = around 5.5</result>


alice and bob drive at constant speeds toward each other on a highway . alice drives at a constant speed of 30 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if alice is 100 km away from bob at 7 am , and also 100 km away from bob at 11 am , then how fast is bob driving ( in kilometers per hour ) ?

Explanation: alice and bob complete 200 km / 4 hours = 50 km / hour bob ' s speed is 50 - 30 = 20 km / hour the answer is a .

subtract(divide(add(100, 100), subtract(11, 7)), 30)

<gadget id="calculator">100 + 100</gadget>
<output>200</output>
<gadget id="calculator">11 - 7</gadget>
<output>4</output>
<gadget id="calculator">200 / 4</gadget>
<output>50</output>
<gadget id="calculator">50 - 30</gadget>
<output>20</output>
<result>20</result>


the calendar of the year 2040 can be used again in the year ?

Explanation: "explanation : given year 2040 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2040 + 28 = 2068 answer : e"

add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2040)

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<gadget id="calculator">14 * 2</gadget>
<output>28</output>
<gadget id="calculator">28 + 2_040</gadget>
<output>2_068</output>
<result>2_068</result>


in what time will a train 100 metres long cross an electic pole , if its speed be 144 km / hr ?

Explanation: "sol . speed = [ 144 x 5 / 18 ] m / sec = 40 m / sec . time taken = ( 100 / 40 ) sec = 2.5 sec . answer a"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 25 hour to row to a place and come back , how far is the place ?

Explanation: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 25 2 x + 3 x = 600 x = 120 km answer is d"

divide(multiply(multiply(subtract(10, 2), add(10, 2)), 25), add(subtract(10, 2), add(10, 2)))

<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">96 * 25</gadget>
<output>2_400</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">2_400 / 20</gadget>
<output>120</output>
<result>120</result>


from a group of 4 boys and 4 girls , 4 children are to be randomly selected . what is the probability that 2 boys and 2 girls will be selected ?

Explanation: "the total number of ways to choose 4 children from 8 is 8 c 4 = 70 the number of ways to choose 2 boys and 2 girls is 4 c 2 * 4 c 2 = 6 * 6 = 36 p ( 2 boys and 2 girls ) = 36 / 70 = 18 / 35 the answer is d ."

divide(multiply(choose(4, const_2), choose(4, const_2)), choose(add(4, 4), 4))

<gadget id="calculator">binomial(4, 2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">binomial(8, 4)</gadget>
<output>70</output>
<gadget id="calculator">36 / 70</gadget>
<output>18/35 = around 0.514286</output>
<result>18/35 = around 0.514286</result>


a can do a work in 8 days . b can do the same work in 24 days . if both a & b are working together in how many days they will finish the work ?

Explanation: "a rate = 1 / 8 b rate = 1 / 24 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 24 ) = 1 / 6 a & b finish the work in 6 days correct option is e"

<gadget id="calculator">8 * 24</gadget>
<output>192</output>
<gadget id="calculator">8 + 24</gadget>
<output>32</output>
<gadget id="calculator">192 / 32</gadget>
<output>6</output>
<result>6</result>


what is the remainder when 50 ! is divided by 16 ^ 8 ? ?

Explanation: "16 raise to 8 = 2 raise to 32 , now highest power of 2 divisible by 50 ! is 25 + 12 + 6 + 3 + 1 = 47 since 2 raise to 47 is divisible , 2 raise to 32 also will be divisible answer : a"

<gadget id="calculator">16 * 50</gadget>
<output>800</output>
<gadget id="calculator">800 % 8</gadget>
<output>0</output>
<result>0</result>


if the cost price of 140 pencils is equal to the selling price of 100 pencils , the gain percent is

Explanation: "let c . p . of each pencil be re . 1 . then , c . p . of 100 pencils = rs . 100 ; s . p . of 100 pencils = rs . 140 . gain % = 40 / 100 * 100 = 40 % answer : e"

divide(const_100, divide(100, subtract(140, 100)))

<gadget id="calculator">140 - 100</gadget>
<output>40</output>
<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">100 / (5/2)</gadget>
<output>40</output>
<result>40</result>


mother , her daughter and her grand child weighs 140 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?

Explanation: "mother + daughter + child = 140 kg daughter + child = 60 kg mother = 140 - 60 = 80 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 80 = 16 kg so now daughter = 140 - ( mother + child ) = 140 - ( 80 + 16 ) = 44 kg answer : a"

subtract(60, divide(subtract(140, 60), 5))

<gadget id="calculator">140 - 60</gadget>
<output>80</output>
<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<gadget id="calculator">60 - 16</gadget>
<output>44</output>
<result>44</result>


a mixture of sand and cement contains , 3 parts of sand and 5 parts of cement . how much of the mixture must be substituted with sand to make the mixture half sand and half cement ?

Explanation: we have total of 8 parts : 3 parts of sand and 5 parts of cement . in order there to be half sand and half cement ( 4 parts of sand and 4 parts of cement ) , we should remove 1 part of cement . with 1 part of cement comes 3 / 5 parts of sand , so we should remove 1 + 3 / 5 = 8 / 5 part of the mixture , which is ( 8 / 5 ) / 8 = 1 / 5 of the mixture . answer : c .

divide(add(const_1, divide(3, 5)), add(5, 3))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">(8/5) / 8</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 24.00 , how much did he pay for it ?

Explanation: let the cost price of book = x selling price of book = 24 $ markup % = 20 ( 120 / 100 ) x = 24 = > x = 20 answer e

subtract(24, multiply(divide(20, const_100), 24))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 24</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">24 - (24/5)</gadget>
<output>96/5 = around 19.2</output>
<result>96/5 = around 19.2</result>


in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 10 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?

Explanation: "the profit 0 f 2009 in terms of 2008 = 0.9 * 15 / 10 * 100 = 135 % c"

multiply(divide(multiply(15, subtract(const_1, divide(10, const_100))), 10), const_100)

<gadget id="calculator">10 / 100</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">15 * (9/10)</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">(27/2) / 10</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(27/20) * 100</gadget>
<output>135</output>
<result>135</result>


find the simple interest on $ 10000 at 6 % per annum for 12 months ?

Explanation: "p = $ 10000 r = 6 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 6 * 1 / 100 = $ 600 answer is c"

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">10_000 * (3/50)</gadget>
<output>600</output>
<result>600</result>


of the 3,600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?

Explanation: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %

multiply(divide(multiply(divide(12, 25), subtract(1, divide(1, 4))), add(multiply(divide(12, 25), subtract(1, divide(1, 4))), subtract(const_1, divide(12, 25)))), const_100)

<gadget id="calculator">12 / 25</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(12/25) * (3/4)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">1 - (12/25)</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">(9/25) + (13/25)</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">(9/25) / (22/25)</gadget>
<output>9/22 = around 0.409091</output>
<gadget id="calculator">(9/22) * 100</gadget>
<output>450/11 = around 40.909091</output>
<result>450/11 = around 40.909091</result>


a man two flats for $ 675958 each . on one he gains 13 % while on the other he loses 13 % . how much does he gain or lose in the whole transaction ?

Explanation: "in such a case there is always a loss loss % = ( 13 / 10 ) ^ 2 = 120 / 71 = 1.69 % answer is a"

multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 13)), 675958), multiply(divide(const_100, subtract(const_100, 13)), 675958))), const_100)