a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 28 m * 2 m * 0.75 m ?

Explanation: "28 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 28 = 1 / 100 * x = > x = 28000 answer : a"

divide(divide(divide(multiply(multiply(multiply(28, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)

<gadget id="calculator">28 * 100</gadget>
<output>2_800</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">2_800 * 200</gadget>
<output>560_000</output>
<gadget id="calculator">0.75 * 100</gadget>
<output>75</output>
<gadget id="calculator">560_000 * 75</gadget>
<output>42_000_000</output>
<gadget id="calculator">42_000_000 / 20</gadget>
<output>2_100_000</output>
<gadget id="calculator">2_100_000 / 10</gadget>
<output>210_000</output>
<gadget id="calculator">210_000 / 7.5</gadget>
<output>28_000</output>
<result>28_000</result>


an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 20286 / - in 3 years at the same rate of interest . find the rate percentage ?

Explanation: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 20286 / - - 17640 / - = rs . 2646 / - rate of interest = ( 2646 / 17640 ) × ( 100 / 1 ) = > 15 % answer : option d"

<gadget id="calculator">20_286 - 17_640</gadget>
<output>2_646</output>
<gadget id="calculator">2_646 / 17_640</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 100</gadget>
<output>15</output>
<result>15</result>


david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 600 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 4,800 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?

Explanation: let the rate be x , then population of the bacteria after each hour can be given as 600,600 x , 600 ( x ^ 2 ) , 600 ( x ^ 3 ) now population at 4 pm = 4800 thus we have 600 ( x ^ 3 ) = 4800 = 8 thus x = 2 therefore population at 3 pm = 600 ( 4 ) = 2400 answer : a

multiply(multiply(power(divide(multiply(multiply(2, 4), 600), 600), const_0_33), 600), power(divide(multiply(multiply(2, 4), 600), 600), const_0_33))

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 600</gadget>
<output>4_800</output>
<gadget id="calculator">4_800 / 600</gadget>
<output>8</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>
<gadget id="calculator">2 * 600</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 * 2</gadget>
<output>2_400</output>
<result>2_400</result>


5 years ago , the average age of a , b , c and d was 45 years . with e joining them now , the average of all the 5 is 50 years . the age of e is ?

Explanation: solution 5 years ago average age of a , b , c , d = 45 years = > 5 years ago total age of a , b , c , d = 45 x 4 = 180 years = > total present age of a , b , c , d = 180 + 5 x 4 = 200 years if e ' s present age is x years = 200 + x / 5 = 50 x = 50 years . answer a

subtract(multiply(50, 5), add(multiply(45, multiply(const_2, const_2)), multiply(5, const_4)))

<gadget id="calculator">50 * 5</gadget>
<output>250</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">180 + 20</gadget>
<output>200</output>
<gadget id="calculator">250 - 200</gadget>
<output>50</output>
<result>50</result>


sandy bought 65 books for $ 1180 from one shop and 55 books for $ 860 from another shop . what is the average price that sandy paid per book ?

Explanation: "average price per book = ( 1180 + 860 ) / ( 65 + 55 ) = 2040 / 120 = $ 17 the answer is c ."

<gadget id="calculator">1_180 + 860</gadget>
<output>2_040</output>
<gadget id="calculator">65 + 55</gadget>
<output>120</output>
<gadget id="calculator">2_040 / 120</gadget>
<output>17</output>
<result>17</result>


there are 15 slate rocks , 20 pumice rocks , and 10 granite rocks randomly distributed in a certain field . if 2 rocks are to be chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?

Explanation: "total no of rocks = 45 probability of choosing 1 st slate rock = 15 / 45 probability of choosing 2 nd slate rock = 14 / 44 ( without replacement ) so combined probability = 15 / 45 * 14 / 44 = 7 / 66 so , answer d ."

multiply(divide(15, add(add(15, 20), 10)), divide(subtract(15, const_1), subtract(add(add(15, 20), 10), const_1)))

<gadget id="calculator">15 + 20</gadget>
<output>35</output>
<gadget id="calculator">35 + 10</gadget>
<output>45</output>
<gadget id="calculator">15 / 45</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">45 - 1</gadget>
<output>44</output>
<gadget id="calculator">14 / 44</gadget>
<output>7/22 = around 0.318182</output>
<gadget id="calculator">(1/3) * (7/22)</gadget>
<output>7/66 = around 0.106061</output>
<result>7/66 = around 0.106061</result>


a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?

Explanation: "net part filled in 1 hour 1 / 4 - 1 / 9 = 5 / 36 the cistern will be filled in 36 / 5 hr = 7.2 hr answer is d"

divide(const_1, subtract(divide(const_1, 4), divide(const_1, 9)))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/4) - (1/9)</gadget>
<output>5/36 = around 0.138889</output>
<gadget id="calculator">1 / (5/36)</gadget>
<output>36/5 = around 7.2</output>
<result>36/5 = around 7.2</result>


approximately how many cubic feet of water are needed to fill a circular swimming pool that is 40 feet across and 7 feet deep ?

Explanation: "answer should be e . v = \ pir ^ 2 h = \ pi * 20 ^ 2 * 7 = approximately 9000"

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">pi * (20 ** 2) * 7</gadget>
<output>2800*pi = around 8_796.45943</output>
<result>2800*pi = around 8_796.45943</result>


( 3 x + 2 ) ( 2 x - 1 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?

Explanation: "expanding we have 6 x ^ 2 - 3 x + 4 x - 2 6 x ^ 2 + x - 2 taking coefficients , a = 6 , k = 1 , n = - 2 therefore a - n + k = 6 - ( - 2 ) + 1 = 8 + 1 = 9 the answer is c ."

add(add(multiply(3, 2), multiply(1, 2)), subtract(multiply(2, 2), multiply(1, 3)))

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<result>9</result>


what is the average ( arithmetic mean ) of 10 , 2030 , 4050 , 6070 , 8090 ?

Explanation: so addition of all term - 10 , 20 , 30 , . . . . . . . 90 so average = ( 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 ) / 9 = ( 450 ) / 9 = 50 hence , the correct answer is e .

subtract(divide(add(add(add(add(10, 2030), 4050), 6070), 8090), add(const_4, const_1)), multiply(multiply(const_100, const_10), const_4))

<gadget id="calculator">10 + 2_030</gadget>
<output>2_040</output>
<gadget id="calculator">2_040 + 4_050</gadget>
<output>6_090</output>
<gadget id="calculator">6_090 + 6_070</gadget>
<output>12_160</output>
<gadget id="calculator">12_160 + 8_090</gadget>
<output>20_250</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">20_250 / 5</gadget>
<output>4_050</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 4</gadget>
<output>4_000</output>
<gadget id="calculator">4_050 - 4_000</gadget>
<output>50</output>
<result>50</result>


the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 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 ) = 1323 3 b 2 = 1323 b 2 = 441 = 21 ( b > 0 ) b = 21 m . answer : d"

<gadget id="calculator">1_323 / 3</gadget>
<output>441</output>
<gadget id="calculator">441 ** (1/2)</gadget>
<output>21</output>
<result>21</result>


after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.3 cubic inches , what is the original volume of the cubic ice , in cubic inches ?

Explanation: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.3 x = 4.8 alternate solution : try to backsolve . initial volume = 4.8 after one hour - - > ( 1 / 4 ) 4.8 = 1.2 after two hours - - > ( 1 / 4 ) 1.2 = 0.3 answer : c"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">0.3 / (1/4)</gadget>
<output>1.2</output>
<gadget id="calculator">1.2 / (1/4)</gadget>
<output>4.8</output>
<result>4.8</result>


the perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm . what is the area of the triangle ?

Explanation: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 3.5 * 22 / 2 = 38.5 cm 2 answer : e"

<gadget id="calculator">(3.5 * 22) / 2</gadget>
<output>38.5</output>
<result>38.5</result>


for a group of n people , k of whom are of the same sex , the ( n - k ) / n expression yields an index for a certain phenomenon in group dynamics for members of that sex . for a group that consists of 20 people , 6 of whom are females , by how much does the index for the females exceed the index for the males in the group ?

Explanation: "index for females = ( 20 - 6 ) / 20 = 7 / 10 = 0.7 index for males = ( 20 - 14 / 20 = 3 / 10 = 0.3 index for females exceeds males by 0.7 - 0.3 = 0.4 answer : a"

subtract(divide(subtract(20, 6), 20), divide(6, 20))

<gadget id="calculator">20 - 6</gadget>
<output>14</output>
<gadget id="calculator">14 / 20</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">6 / 20</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(7/10) - (3/10)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


x does a work in 40 days . y does the same work in 60 days . in how many days they together will do the same work ?

Explanation: "x ' s 1 day ' s work = 1 / 40 y ' s 1 day ' s work = 1 / 60 ( x + y ) ' s 1 day ' s work = ( 1 / 40 + 1 / 60 ) = 1 / 24 both together will finish the work in 24 days . correct option is c"

inverse(add(divide(const_1, 40), divide(const_1, 60)))

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(1/40) + (1/60)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>24</result>


the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the sum and the number if the ratio between the digits of the number is 1 : 2 ?

Explanation: "let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b"

multiply(divide(36, subtract(multiply(subtract(const_10, 1), multiply(2, 1)), subtract(const_10, 1))), 2)

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">18 - 9</gadget>
<output>9</output>
<gadget id="calculator">36 / 9</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>8</result>


7 carpet - weavers can weave 7 carpets in 7 days . at the same rate , how many carpets would be woven by 14 carpet - weavers in 14 days ?

Explanation: explanation : solution : let the required number of carpets be x . more weavers , more carpets ( direct proportion ) more days , more carpets ( direct proportion ) weavers 7 : 14 } : : 7 : x days 7 : 14 . ' . 7 * 7 * x = 14 * 14 * 7 < = > x = 14 * 14 * 7 / 7 * 7 = 28 . answer : b

<gadget id="calculator">7 + 7</gadget>
<output>14</output>
<gadget id="calculator">14 + 14</gadget>
<output>28</output>
<result>28</result>


what is the speed of the stream if a canoe rows upstream at 6 km / hr and downstream at 12 km / hr

Explanation: "sol . speed of stream = 1 / 2 ( 12 - 6 ) kmph = 3 kmph . answer c"

<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<result>3</result>


a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 40 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?

Explanation: i year best is to give a number to his income , say 100 . . and let saving be x . . so expenditure = 100 - x next year - income = 140 savings = 2 x expenditure = 140 - 2 x . . now 140 - 2 x + 100 - x = 2 ( 100 - x ) . . . 240 - 3 x = 200 - 2 x . . . . . . . . . . . . . . . . x = 40 . . . saving % = 40 / 100 * 100 = 40 % answer : b

multiply(divide(subtract(add(add(100, 40), 100), multiply(2, 100)), const_100), const_100)

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 + 100</gadget>
<output>240</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">240 - 200</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>


a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 587.75 . how many boxes of plain cookies did she sell ?

Explanation: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1587.75 = > x = 787 e"

<gadget id="calculator">1_000 + 587.75</gadget>
<output>1_587.75</output>
<gadget id="calculator">1_587.75 / 2</gadget>
<output>793.875</output>
<result>793.875</result>


find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 10 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 10 5 x = 1355 x = 271 large number = 271 + 1365 = 1636 a"

multiply(divide(subtract(1365, 10), subtract(6, const_1)), 6)

<gadget id="calculator">1_365 - 10</gadget>
<output>1_355</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_355 / 5</gadget>
<output>271</output>
<gadget id="calculator">271 * 6</gadget>
<output>1_626</output>
<result>1_626</result>


two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every fourth , starting with the fourth , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?

Explanation: widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 19 + 24 - 9 = 34 hence , widgets not inspected : 98 - 34 = 64 option d

subtract(98, subtract(add(floor(divide(98, add(const_4, const_1))), floor(divide(98, const_4))), floor(divide(98, add(const_10, add(const_4, const_1))))))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">98 / 5</gadget>
<output>98/5 = around 19.6</output>
<gadget id="calculator">floor(98/5)</gadget>
<output>19</output>
<gadget id="calculator">98 / 4</gadget>
<output>49/2 = around 24.5</output>
<gadget id="calculator">floor(49/2)</gadget>
<output>24</output>
<gadget id="calculator">19 + 24</gadget>
<output>43</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">98 / 15</gadget>
<output>98/15 = around 6.533333</output>
<gadget id="calculator">floor(98/15)</gadget>
<output>6</output>
<gadget id="calculator">43 - 6</gadget>
<output>37</output>
<gadget id="calculator">98 - 37</gadget>
<output>61</output>
<result>61</result>


the length of the bridge , which a train 130 metres long and travelling at 36 km / hr can cross in 45 seconds , is :

Explanation: "speed = [ 36 x 5 / 18 ] m / sec = 10 m / sec time = 45 sec let the length of bridge be x metres . then , ( 130 + x ) / 45 = 10 = > 130 + x = 450 = > x = 320 m . answer : a"

subtract(multiply(divide(multiply(36, speed(const_1000, const_1)), speed(const_3600, const_1)), 45), 130)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">36_000 / 3_600</gadget>
<output>10</output>
<gadget id="calculator">10 * 45</gadget>
<output>450</output>
<gadget id="calculator">450 - 130</gadget>
<output>320</output>
<result>320</result>


the speed of a car increases by 2 kms after every one hour . if the distance travelled in the first one hour was 35 kms , what was the total distance travelled in 12 hours ?

Explanation: "total distance travelled in 12 hours = ( 35 + 37 + 39 + . . . upto 12 terms ) . this is an a . p . with first term , a = 35 , number of terms , n = 12 , common difference d = 2 required distance = 12 / 2 ( 2 * 35 + ( 12 - 1 ) * 2 ) = 6 ( 70 + 22 ) = 552 km . correct option : c"

multiply(add(multiply(2, 35), multiply(subtract(12, const_1), 2)), divide(12, 2))

<gadget id="calculator">2 * 35</gadget>
<output>70</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">70 + 22</gadget>
<output>92</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">92 * 6</gadget>
<output>552</output>
<result>552</result>


a money lender lent rs . 1000 at 4 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .

Explanation: ( 1000 xtx 4 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 â † ’ t = 3.2 answer a

divide(350, add(divide(multiply(4, 1000), const_100), divide(multiply(1400, 5), const_100)))

<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 100</gadget>
<output>40</output>
<gadget id="calculator">1_400 * 5</gadget>
<output>7_000</output>
<gadget id="calculator">7_000 / 100</gadget>
<output>70</output>
<gadget id="calculator">40 + 70</gadget>
<output>110</output>
<gadget id="calculator">350 / 110</gadget>
<output>35/11 = around 3.181818</output>
<result>35/11 = around 3.181818</result>


for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 90 θ 33 ) θ 17 ) - ( 97 θ ( 33 θ 17 ) ) ?

Explanation: ( ( 90 θ 33 ) θ 17 ) the remainder of 90 divided by 33 is 24 ; the remainder of 24 divided by 17 is 7 ; ( 97 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 97 divided by 16 is 1 . 7 - 1 = 6 . answer : d .

subtract(reminder(reminder(90, 33), 17), reminder(97, reminder(33, 17)))

<gadget id="calculator">90 % 33</gadget>
<output>24</output>
<gadget id="calculator">24 % 17</gadget>
<output>7</output>
<gadget id="calculator">33 % 17</gadget>
<output>16</output>
<gadget id="calculator">97 % 16</gadget>
<output>1</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<result>6</result>


if 1,000 microns = 1 decimeter , and 1,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?

Explanation: "given that 1,000 microns = 1 decimeter = 1,000 , 000,000 angstroms so , 1 micron = 1,000 , 000,000 / 1,000 = 1 , 000,000 answer : c"

multiply(divide(1, multiply(const_100, const_100)), multiply(const_100, const_100))

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">1 / 10_000</gadget>
<output>1/10_000 = around 0.0001</output>
<gadget id="calculator">(1/10_000) * 10_000</gadget>
<output>1</output>
<result>1</result>


if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of $ 8400 ?

Explanation: "required difference = [ 3 1 / 2 % of $ 8400 ] – [ 3 1 / 3 % of $ 8400 ] = [ ( 7 / 20 ) - ( 10 / 3 ) ] % of $ 8400 = 1 / 6 % of $ 8400 = $ [ ( 1 / 6 ) * ( 1 / 100 ) * 8400 ] = $ 14 . answer a ."

divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 8400), const_100)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 3</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) + 3</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(7/2) - (10/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 8_400</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 / 100</gadget>
<output>14</output>
<result>14</result>


machine p and machine q are each used to manufacture 770 sprockets . it takes machine p 10 hours longer to produce 770 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?

Explanation: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 770 / x = 770 / 1.1 x + 10 1.1 ( 770 ) = 770 + 11 x 11 x = 77 x = 7 the answer is c ."

divide(subtract(770, divide(770, add(divide(10, const_100), const_1))), 10)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">770 / (11/10)</gadget>
<output>700</output>
<gadget id="calculator">770 - 700</gadget>
<output>70</output>
<gadget id="calculator">70 / 10</gadget>
<output>7</output>
<result>7</result>


the c . p of 20 books is equal to the s . p of 30 books . find his gain % or loss % ?

Explanation: explanation : 20 cp = 30 sp 30 - - - 10 cp loss 100 - - - ? = > 33.33 % loss answer : c

multiply(subtract(const_1, divide(20, 30)), const_100)

<gadget id="calculator">20 / 30</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">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


weights of two friends ram and shyam are in the ratio 3 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?

Explanation: "solution : given ratio of ram and shayam ' s weight = 3 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 3 / 5 or , x = 18 % . answer : option a"

add(15, multiply(subtract(15, 10), divide(3, 5)))

<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">5 * (3/5)</gadget>
<output>3</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<result>18</result>


in the manufacture of a certain product , 7 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

Explanation: "percent of defective produced = 7 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 7 / 100 ) * 100 % = ( 28 / 10000 ) * 100 % = ( 28 / 100 ) % = . 28 % answer b"

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">7 * (1/25)</gadget>
<output>7/25 = around 0.28</output>
<result>7/25 = around 0.28</result>


a trader bought a car at 30 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 70 s = 70 * ( 180 / 100 ) = 126 100 - 126 = 26 % answer : b"

multiply(subtract(divide(divide(multiply(subtract(const_100, 30), add(const_100, 80)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">70 * 180</gadget>
<output>12_600</output>
<gadget id="calculator">12_600 / 100</gadget>
<output>126</output>
<gadget id="calculator">126 / 100</gadget>
<output>63/50 = around 1.26</output>
<gadget id="calculator">(63/50) - 1</gadget>
<output>13/50 = around 0.26</output>
<gadget id="calculator">(13/50) * 100</gadget>
<output>26</output>
<result>26</result>


a boy goes to his school from his house at a speed of 3 km / hr and return at a speed of 2 km / hr . if he takes 5 hours in going and coming , the distance between his house and school is ?

Explanation: average speed = 2 * 3 * 2 / 3 + 2 = 12 / 5 km / hr distance traveled = 12 / 5 * 5 = 12 km distance between house and school = 12 / 2 = 6 km answer is b

multiply(divide(5, add(divide(3, 2), const_1)), 3)

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) + 1</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">5 / (5/2)</gadget>
<output>2</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<result>6</result>


how many seconds will a 600 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

Explanation: let length of tunnel is x meter distance = 600 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 600 + x = ( 65 / 3 ) * 60 600 + x = 20 * 65 = 1300 x = 1300 - 600 = 700 meters answer : a

multiply(multiply(subtract(divide(600, multiply(subtract(63, 3), const_0_2778)), const_1), const_10), const_2)

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">600 / (50/3)</gadget>
<output>36</output>
<gadget id="calculator">36 - 1</gadget>
<output>35</output>
<gadget id="calculator">35 * 10</gadget>
<output>350</output>
<gadget id="calculator">350 * 2</gadget>
<output>700</output>
<result>700</result>


a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?

Explanation: a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 c ' s 1 hour work = ( 7 / 12 - 1 / 2 ) = 1 / 12 c alone will take 12 hours to do the work . answer : a

divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) - (1/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 60 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

Explanation: "total = 75 books . 60 % of books that were loaned out are returned - - > 100 % - 60 % = 40 % of books that were loaned out are not returned . now , there are 68 books , thus 75 - 65 = 10 books are not returned . { loaned out } * 0.4 = 10 - - > { loaned out } = 25 . answer : b ."

divide(subtract(75, 65), subtract(const_1, divide(60, const_100)))

<gadget id="calculator">75 - 65</gadget>
<output>10</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">10 / (2/5)</gadget>
<output>25</output>
<result>25</result>


cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost q is what percent of the original cost ?

Explanation: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"

<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>
<result>1_600</result>


albert is 2 times mary ’ s age and 4 times as old as betty . mary is 12 years younger than albert . how old is betty ?

Explanation: "a = 2 m = m + 12 m = 12 a = 24 a = 4 b , and so b = 6 the answer is a ."

<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<result>6</result>


what is the next number : 2 , 10 , 82 , __

Explanation: "3 ^ 0 + 1 = 2 3 ^ 2 + 1 = 10 3 ^ 4 + 1 = 82 3 ^ 6 + 1 = 730 the answer is b ."

subtract(subtract(subtract(multiply(82, const_10), const_100), 2), 2)

<gadget id="calculator">82 * 10</gadget>
<output>820</output>
<gadget id="calculator">820 - 100</gadget>
<output>720</output>
<gadget id="calculator">720 - 2</gadget>
<output>718</output>
<gadget id="calculator">718 - 2</gadget>
<output>716</output>
<result>716</result>


marts income is 50 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income

Explanation: m = ( 150 / 100 ) t t = ( 60 / 100 ) j = > m = ( 90 / 100 ) j answer d .

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

<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 100</gadget>
<output>500/3 = around 166.666667</output>
<gadget id="calculator">150 / (500/3)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 100</gadget>
<output>90</output>
<result>90</result>


what least number should be subtracted from 13601 such that the remainder is divisible by 87 ?

Explanation: "13601 ÷ 87 = 156 , remainder = 29 hence 29 is the least number which can be subtracted from 13601 such that the remainder is divisible by 87 answer is b"

<gadget id="calculator">13_601 % 87</gadget>
<output>29</output>
<result>29</result>


if the complement of a certain angle is 7 times the measure of that certain angle , then what is the measure of that certain angle ?

Explanation: thecomplementof angle a is the angle which , when added to angle a , gives 90 degrees . the two acute angles of a right triangle are complements , for example . the original angle is x , so the complement is 7 x , and together , these add up to 90 degrees . x + 7 x = 90 8 x = 90 x = 11.25 ° answer = ( e )

divide(subtract(const_100, const_10), add(7, const_1))

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">90 / 8</gadget>
<output>45/4 = around 11.25</output>
<result>45/4 = around 11.25</result>


the area of a triangle is with base 2 m and height 5 m ?

Explanation: "1 / 2 * 2 * 5 = 5 m 2 answer : e"

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


ramu bought an old car for rs . 38000 . he spent rs . 12000 on repairs and sold it for rs . 64900 . what is his profit percent ?

Explanation: "total cp = rs . 38000 + rs . 12000 = rs . 50000 and sp = rs . 64900 profit ( % ) = ( 64900 - 50000 ) / 50000 * 100 = 29.8 % answer : e"

<gadget id="calculator">38_000 + 12_000</gadget>
<output>50_000</output>
<gadget id="calculator">64_900 - 50_000</gadget>
<output>14_900</output>
<gadget id="calculator">14_900 / 50_000</gadget>
<output>149/500 = around 0.298</output>
<gadget id="calculator">(149/500) * 100</gadget>
<output>149/5 = around 29.8</output>
<result>149/5 = around 29.8</result>


alfred buys an old scooter for $ 4700 and spends $ 800 on its repairs . if he sells the scooter for $ 6400 , his gain percent is ?

Explanation: "c . p . = 4700 + 800 = $ 5500 s . p . = $ 6400 gain = 6400 - 5500 = $ 900 gain % = 900 / 5500 * 100 = 16.36 % answer is b"

<gadget id="calculator">4_700 + 800</gadget>
<output>5_500</output>
<gadget id="calculator">6_400 - 5_500</gadget>
<output>900</output>
<gadget id="calculator">900 / 5_500</gadget>
<output>9/55 = around 0.163636</output>
<gadget id="calculator">(9/55) * 100</gadget>
<output>180/11 = around 16.363636</output>
<result>180/11 = around 16.363636</result>


Explanation: let 4207 - x = 3007 then x = 4207 - 3007 = 1200 answer is d

<gadget id="calculator">3_251 + 587</gadget>
<output>3_838</output>
<gadget id="calculator">3_838 + 369</gadget>
<output>4_207</output>
<gadget id="calculator">4_207 - 3_007</gadget>
<output>1_200</output>
<result>1_200</result>


the manufacturer ’ s suggested retail price ( msrp ) of a certain item is $ 60 . store a sells the item for 20 percent more than the msrp . the regular price of the item at store b is 30 percent more than the msrp , but the item is currently on sale for 10 percent less than the regular price . if sales tax is 5 percent of the purchase price at both stores , what is the result when the total cost of the item at store b is subtracted from the total cost of the item at store a ?

Explanation: msrp = 60 price at store a = 60 ∗ 120100 = 72 = 60 ∗ 120100 = 72 price at store b = 60 ∗ 130100 ∗ 90100 = 70.2 = 60 ∗ 130100 ∗ 90100 = 70.2 difference = 72.0 - 70.2 = 1.8 sales tax applicable = 5 % on both = 1.8 + 0.09 = 1.89 answer = d

subtract(multiply(60, divide(add(const_100, 20), const_100)), multiply(divide(subtract(const_100, 10), const_100), multiply(divide(add(const_100, 30), const_100), 60)))

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">60 * (6/5)</gadget>
<output>72</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) * 60</gadget>
<output>78</output>
<gadget id="calculator">(9/10) * 78</gadget>
<output>351/5 = around 70.2</output>
<gadget id="calculator">72 - (351/5)</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>


if the selling price of 100 articles is equal to the cost price of 63 articles , then the loss or gain percent is :

Explanation: "let c . p . of each article be re . 1 . then , c . p . of 100 articles = rs . 100 ; s . p . of 100 articles = rs . 63 . loss % = 37 / 100 * 100 = 37 % answer : e"

<gadget id="calculator">100 - 63</gadget>
<output>37</output>
<result>37</result>


rs . 1775 is divided amongst a , b , c so that 5 times a ' s share , 3 times b ' s share and 7 times c ' s share are all equal . find c ' s share ?

Explanation: a + b + c = 590 5 a = 3 b = 7 c = x a : b : c = 1 / 5 : 1 / 3 : 1 / 7 = 21 : 35 : 15 15 / 71 * 1775 = rs . 375 answer : e

divide(1775, add(add(divide(7, 5), divide(7, 3)), const_1))

<gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">(7/5) + (7/3)</gadget>
<output>56/15 = around 3.733333</output>
<gadget id="calculator">(56/15) + 1</gadget>
<output>71/15 = around 4.733333</output>
<gadget id="calculator">1_775 / (71/15)</gadget>
<output>375</output>
<result>375</result>


n ^ ( n / 2 ) = 2 is true when n = 2 in the same way what is the value of n if n ^ ( n / 2 ) = 4 ?

Explanation: "n ^ ( n / 2 ) = 4 apply log n / 2 logn = log 4 nlogn = 2 log 4 = log 4 ^ 2 = log 16 logn = log 16 now apply antilog n = 16 / n now n = 4 . answer : c"

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<result>4</result>


if a - b = 3 and a ( power 2 ) + b ( power 2 ) = 23 , find the value of ab .

Explanation: "2 ab = ( a ( power 2 ) + b ( power 2 ) - ( a - b ) ( power 2 ) = 23 - 9 = 14 ab = 7 . answer is c ."

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">23 - 9</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>


a person buys an article at $ 380 . at what price should he sell the article so as to make a profit of 25 % ?

Explanation: "c 475 cost price = $ 380 profit = 25 % of 380 = $ 95 selling price = cost price + profit = 380 + 95 = 475"

add(380, multiply(380, divide(25, const_100)))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">380 * (1/4)</gadget>
<output>95</output>
<gadget id="calculator">380 + 95</gadget>
<output>475</output>
<result>475</result>


in certain code ' twice ' is written as ' 34 $ 5 δ ' and ' wears ' is written as ' 4 δ 29 % ' . how is ' seat ' written in that code ?

Explanation: answer : option b

<gadget id="calculator">29 - 5</gadget>
<output>24</output>
<gadget id="calculator">24 - 1</gadget>
<output>23</output>
<result>23</result>


the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12.5 percent , what was the annual interest rate last year ?

Explanation: "12.5 = 1.1 * x x = 11.36 % answer d )"

divide(multiply(12.5, const_100), add(12.5, const_100))

<gadget id="calculator">12.5 * 100</gadget>
<output>1_250</output>
<gadget id="calculator">12.5 + 100</gadget>
<output>112.5</output>
<gadget id="calculator">1_250 / 112.5</gadget>
<output>11.111111</output>
<result>11.111111</result>


two pipes a and b can fill a cistern in 10 and 15 minutes respectively . both fill pipes are opened together , but at the end of 3 minutes , ‘ b ’ is turned off . how much time will the cistern take to fill ?

Explanation: in one min , ( a + b ) fill the cistern = 1 ⁄ 10 + 1 ⁄ 15 = 1 ⁄ 6 th in 3 min , ( a + b ) fill the cistern = 3 ⁄ 6 = 1 ⁄ 2 th remaining part = 1 - 1 ⁄ 2 = 1 ⁄ 2 ∵ 1 ⁄ 10 th part filled by a in one min . ∴ 1 ⁄ 2 nd part filled by a in 10 × 1 ⁄ 2 = 5 min . ∴ total time = 3 + 5 = 8 min . answer b

add(multiply(10, subtract(const_1, multiply(add(inverse(10), inverse(15)), const_3))), 3)

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/10) + (1/15)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 3</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">10 * (1/2)</gadget>
<output>5</output>
<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<result>8</result>


a swimmer can swim in still water at 4 km / h . if the speed of the water current is 2 km / h , how many hours will the swimmer take to swim against the current for 8 km ?

Explanation: "the swimmer can swim against the current at a speed of 4 - 2 = 2 km / h . the time it will take is 8 / 2 = 4 hours . the answer is d ."

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


Explanation: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 ) = 77 note : 1 is not a prime number option d

add(add(8, add(add(add(const_2, const_3), const_2), const_4)), add(add(add(add(add(add(add(add(add(add(add(const_2, const_3), const_2), const_4), const_2), const_4), add(add(add(add(const_2, const_3), const_2), const_4), const_2)), add(add(add(const_2, const_3), const_2), const_4)), add(add(const_2, const_3), const_2)), add(const_2, const_3)), const_3), const_2))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">8 + 11</gadget>
<output>19</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<gadget id="calculator">13 + 4</gadget>
<output>17</output>
<gadget id="calculator">17 + 13</gadget>
<output>30</output>
<gadget id="calculator">30 + 11</gadget>
<output>41</output>
<gadget id="calculator">41 + 7</gadget>
<output>48</output>
<gadget id="calculator">48 + 5</gadget>
<output>53</output>
<gadget id="calculator">53 + 3</gadget>
<output>56</output>
<gadget id="calculator">56 + 2</gadget>
<output>58</output>
<gadget id="calculator">19 + 58</gadget>
<output>77</output>
<result>77</result>


a jogger running at 9 km / hr along side a railway track is 290 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?

Explanation: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 290 + 120 = 410 m . time taken = 410 / 10 = 41 sec . answer : e"

divide(add(290, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

<gadget id="calculator">290 + 120</gadget>
<output>410</output>
<gadget id="calculator">45 - 9</gadget>
<output>36</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">410 / 10</gadget>
<output>41</output>
<result>41</result>


working simultaneously and independently at an identical constant rate , 20 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 8 days ?

Explanation: "the rate of 20 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 20 * ( x / 4 ) = x / 80 units per day ; now , again as { time } * { combined rate } = { job done } then 8 * ( m * x / 80 ) = 3 x - - > m = 30 . answer : a ."

<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">60 * (1/2)</gadget>
<output>30</output>
<result>30</result>


the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive .

Explanation: we ' re dealing with a sequence of consecutive odd integers : 13 to 31 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 31 = 44 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 29 = 44 now we have proof that there is no middle term . we have 5 bunches of 44 5 ( 44 ) = 220 a

subtract(power(divide(add(31, const_1), 2), const_2), power(divide(add(subtract(13, 2), const_1), 2), 2))

<gadget id="calculator">31 + 1</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">13 - 2</gadget>
<output>11</output>
<gadget id="calculator">11 + 1</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">256 - 36</gadget>
<output>220</output>
<result>220</result>


if o is the center of the circle in the figure above and the area of the unshaded sector is 5 , what is the area of the shaded region ?

Explanation: 60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d

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


if a mixture is 5 ⁄ 9 alcohol by volume and 4 ⁄ 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?

Explanation: "should be a sub - 600 level q . . volume = { 5 / 9 } / { 4 / 9 } = 5 / 4 c"

<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">4 / 9</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(5/9) / (4/9)</gadget>
<output>5/4 = around 1.25</output>
<result>5/4 = around 1.25</result>


two spherical balls lie on the ground touching . if one of the balls has a radius of 8 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ( in centimeters ) ?

Explanation: "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 8 = ( r - 12 ) / r 4 r = 8 r - 96 r = 24 the answer is b ."

<gadget id="calculator">4 + 12</gadget>
<output>16</output>
<gadget id="calculator">16 + 8</gadget>
<output>24</output>
<result>24</result>


s = { 12 , 35 , 69 } t = { 45 , 67 , 13 } what is the probability that x chosen from s and y chosen from t will result x * y = even

Explanation: p : the probability that x * y is even , then p = 1 - p ( x * y is odd ) p ( x * y odd ) = p ( x odd ) * p ( y odd ) = 4 / 6 * 4 / 6 = 16 / 36 = 4 / 9 and p = 1 - 4 / 9 = 5 / 9 option : a

divide(add(divide(12, const_4), const_2), multiply(divide(12, const_4), divide(12, const_4)))

<gadget id="calculator">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">5 / 9</gadget>
<output>5/9 = around 0.555556</output>
<result>5/9 = around 0.555556</result>


a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 110 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?

Explanation: "solution provided by stanford 2012 is correct : 110 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 110 / 800 * 1 / 600 = 311 / 48,000 . answer : a ."

multiply(divide(110, 800), divide(const_1, 600))

<gadget id="calculator">110 / 800</gadget>
<output>11/80 = around 0.1375</output>
<gadget id="calculator">1 / 600</gadget>
<output>1/600 = around 0.001667</output>
<gadget id="calculator">(11/80) * (1/600)</gadget>
<output>11/48_000 = around 0.000229</output>
<result>11/48_000 = around 0.000229</result>


a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ?

Explanation: "probability = ( favorable cases ) / ( total number of cases ) total number of ways in which a person can ride car = 3 * 3 * 3 = 27 ( in first ride he has 3 options to sit , in second right again he has 3 seats available to sit and so on ) number of favorable cases , i . e . , when he rides on different cars ; he can choose seat car in 3 ways in his 1 st ride . he can choose seat car in 2 ways in his 2 nd ride . he can choose seat car in 1 ways in his 3 rd ride . so , 3 * 2 * 1 = 6 ways thus , probability of choosing different seats = 6 / 27 = 2 / 9 answer : c"

multiply(factorial(3), power(divide(1, 3), 3))

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) ** 3</gadget>
<output>1/27 = around 0.037037</output>
<gadget id="calculator">6 * (1/27)</gadget>
<output>2/9 = around 0.222222</output>
<result>2/9 = around 0.222222</result>


a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 20 gallons of water and 40 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?

Explanation: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 40 gallons salt is added and 20 gallons of water is added . so salt now becomes - > ( 0.2 x + 40 ) and water - - > ( 0.6 x + 20 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 40 ) = ( 0.6 x + 20 ) / 2 = > 0.4 x + 80 = 0.6 x + 20 = > 0.2 x = 60 solving , x = 300 answer : a"

divide(subtract(multiply(40, const_2), 20), subtract(subtract(subtract(1, divide(20, const_100)), multiply(subtract(1, divide(20, const_100)), divide(1, const_4))), multiply(const_2, divide(20, const_100))))

<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">80 - 20</gadget>
<output>60</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">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(4/5) * (1/4)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(4/5) - (1/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 * (1/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">60 / (1/5)</gadget>
<output>300</output>
<result>300</result>


a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area w covered by the two roads ?

Explanation: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads w = 1000 + 600 - 25 = 1575 answer : option c"

add(rectangle_area(200, 5), rectangle_area(120, 5))

<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<gadget id="calculator">120 * 5</gadget>
<output>600</output>
<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>
<result>1_600</result>


the diagonals of a rhombus are 18 cm and 22 cm . find its area ?

Explanation: 1 / 2 * 18 * 22 = 198 answer : c

<gadget id="calculator">(18 * 22) / 2</gadget>
<output>198</output>
<result>198</result>


if 20 liters of chemical x are added to 80 liters of a mixture that is 25 % chemical x and 75 % chemical y , then what percentage of the resulting mixture is chemical x ?

Explanation: the amount of chemical x in the solution is 20 + 0.25 ( 80 ) = 40 liters . 40 liters / 100 liters = 40 % the answer is d .

add(20, multiply(divide(25, const_100), 80))

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


a number increased by 20 % gives 600 . the number is

Explanation: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 600 ( 120 × 5 = 600 ) 100 % - - - - - - - > 500 ( 100 × 5 = 500 ) d )"

divide(600, add(const_1, divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">600 / (6/5)</gadget>
<output>500</output>
<result>500</result>


when a laptop is sold for rs . 49,000 , the owner loses 30 % . at what price must that laptop be sold in order to gain 30 % ?

Explanation: 70 : 49000 = 130 : x x = ( 49000 x 130 ) / 70 = 91000 . hence , s . p . = rs . 91,000 . answer : option e

multiply(divide(multiply(multiply(multiply(add(const_3, const_4), add(const_3, const_4)), const_100), multiply(add(const_3, const_2), const_2)), subtract(const_100, 30)), add(const_100, 30))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">49 * 100</gadget>
<output>4_900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">4_900 * 10</gadget>
<output>49_000</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">49_000 / 70</gadget>
<output>700</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">700 * 130</gadget>
<output>91_000</output>
<result>91_000</result>


if a and b together can finish a work in 16 days . a can finish same work alone in 24 days then b alone can finish same work alone in how many days ?

Explanation: ( a + b ) work in 1 day = 1 / 16 , a work in 1 day = 1 / 24 b work in 1 day = [ 1 / 16 - 1 / 24 ] = 1 / 48 . b alone can finish same work in 48 days . answer b

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/16) - (1/24)</gadget>
<output>1/48 = around 0.020833</output>
<gadget id="calculator">1 / (1/48)</gadget>
<output>48</output>
<result>48</result>


if 5 a + 7 b = m , where a and b are positive integers , what is the largest possible value of m for which exactly one pair of integers ( a , b ) makes the equation true ?

Explanation: 5 * a 1 + 7 * b 1 = m 5 * a 2 + 7 * b 2 = m 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 toawe will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 froma , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer

add(multiply(7, add(const_3, const_4)), multiply(5, const_4))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">49 + 20</gadget>
<output>69</output>
<result>69</result>


the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 15 % ?

Explanation: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 85 gain % = 21 / 64 * 100 = 32.8 % . answer : a"

multiply(subtract(divide(subtract(const_100, 15), 64), const_1), const_100)

<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 64</gadget>
<output>85/64 = around 1.328125</output>
<gadget id="calculator">(85/64) - 1</gadget>
<output>21/64 = around 0.328125</output>
<gadget id="calculator">(21/64) * 100</gadget>
<output>525/16 = around 32.8125</output>
<result>525/16 = around 32.8125</result>


the calendar of the year 2028 can be used again in the year ?

Explanation: "explanation : given year 2028 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 , 2028 + 28 = 2056 answer : c"

add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2028)

<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_028</gadget>
<output>2_056</output>
<result>2_056</result>


a man speaks truth 3 out of 4 times . he throws a die and reports it to be a 6 . what is the probability of it being a 6 ?

Explanation: explanation : there are two cases 1 ) he is telling truth that the die reports 6 , its probability = 3 / 4 * 1 / 6 = 1 / 8 2 ) he is telling lie that the die reports 6 , its probability = 1 / 4 * 5 / 6 = 5 / 24 so required probability = ( 1 / 8 ) / ( 1 / 8 ) + ( 5 / 24 ) = ( 1 / 8 ) / ( 1 / 3 ) = 3 / 8 hencer ( d ) is the correct answer answer : d

divide(multiply(divide(3, 4), divide(const_1, 6)), add(multiply(divide(3, 4), divide(const_1, 6)), multiply(divide(const_1, const_4), divide(const_5, 6))))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(3/4) * (1/6)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(1/4) * (5/6)</gadget>
<output>5/24 = around 0.208333</output>
<gadget id="calculator">(1/8) + (5/24)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/8) / (1/3)</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


on a sum of money , simple interest for 2 years is rs 660 and compound interest is rs 696.30 , the rate of interest being the same in both cases .

Explanation: explanation : difference between c . i and s . i for 2 years = 36.30 s . i . for one year = 330 . s . i . on rs 330 for one year = 36.30 so r % = \ frac { 100 * 36.30 } { 330 * 1 } = 11 % answer : d

multiply(divide(multiply(subtract(696.3, 660), 2), 660), const_100)

<gadget id="calculator">696.3 - 660</gadget>
<output>36.3</output>
<gadget id="calculator">36.3 * 2</gadget>
<output>72.6</output>
<gadget id="calculator">72.6 / 660</gadget>
<output>0.11</output>
<gadget id="calculator">0.11 * 100</gadget>
<output>11</output>
<result>11</result>


an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 19404 / - in 3 years at the same rate of interest . find the rate percentage ?

Explanation: explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 19404 / - - 17640 / - = rs . 1764 / - rate of interest = ( 1764 / 17640 ) × ( 100 / 1 ) = > 10 % answer : option d

<gadget id="calculator">19_404 - 17_640</gadget>
<output>1_764</output>
<gadget id="calculator">1_764 / 17_640</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :

Explanation: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 x = 20 . answer : c"

divide(subtract(22, 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">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<result>20</result>


if y > 0 , ( 10 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

Explanation: "can be reduced to y / 2 + 3 y / 10 = 4 y / 5 = 80 % e"

multiply(const_100, add(divide(10, 20), divide(3, 10)))

<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/2) + (3/10)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 * (4/5)</gadget>
<output>80</output>
<result>80</result>


let the number which when multiplied by 11 is increased by 300 .

Explanation: solution let the number be x . then , 11 x - x = 300 ‹ = › 10 x = 300 x ‹ = › 30 . answer e

<gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">300 / 10</gadget>
<output>30</output>
<result>30</result>


in a division , a student took 78 as divisor instead of 36 . his answer was 24 . the correct answer is -

Explanation: "x / 78 = 24 . x = 24 * 78 . so correct answer would be , ( 24 * 78 ) / 36 = 52 . answer : d"

<gadget id="calculator">78 * 24</gadget>
<output>1_872</output>
<gadget id="calculator">1_872 / 36</gadget>
<output>52</output>
<result>52</result>


an athlete takes 10 seconds to run 100 m . what is his avg . speed in miles per hour ?

Explanation: his average speed is 10 m / s . which is 36 km / hr . but 36 km = 22.37 miles . the average speed of the athlete is 22.37 mph answer : a

divide(multiply(divide(100, const_1000), const_0_6), divide(10, const_3600))

<gadget id="calculator">100 / 1_000</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(1/10) * (3/5)</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>
<gadget id="calculator">(3/50) / (1/360)</gadget>
<output>108/5 = around 21.6</output>
<result>108/5 = around 21.6</result>


a pair of articles was bought for $ 50 at a discount of 50 % . what must be the marked price of each of the article ?

Explanation: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 50 % of x = 25 x = 25 * . 5 = $ 12.50 answer is b"

divide(multiply(subtract(const_100, 50), divide(50, const_2)), const_100)

<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">50 * 25</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?

Explanation: the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 6 hours , the amount of water is 3.6 - 0.5 ( 6 ) = 0.6 gallons the concentration of water is 0.6 / ( 2.4 + 0.6 ) = 2 / 10 = 20 % the answer is b .

multiply(divide(subtract(divide(multiply(6, subtract(const_100, 40)), const_100), multiply(0.5, 6)), subtract(6, multiply(0.5, 6))), const_100)

<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<gadget id="calculator">360 / 100</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">0.5 * 6</gadget>
<output>3</output>
<gadget id="calculator">(18/5) - 3</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">6 - 3</gadget>
<output>3</output>
<gadget id="calculator">(3/5) / 3</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.75 per kg , so that the mixture be worth rs 3.25 a kg ?

Explanation: c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.75 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.75 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.50 ) / ( 0.15 ) = 10 / 3 c

<gadget id="calculator">3.75 - 3.25</gadget>
<output>0.5</output>
<gadget id="calculator">3.25 - 3.1</gadget>
<output>0.15</output>
<gadget id="calculator">0.5 / 0.15</gadget>
<output>3.333333</output>
<result>3.333333</result>


a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 256 sq . feet , how many feet of fencing will be required ?

Explanation: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 256 breadth = 12.8 feet area to be fenced = 2 b + l = 2 ( 12.8 ) + 20 = 45.6 feet answer : a"

add(multiply(divide(256, 20), const_2), 20)

<gadget id="calculator">256 / 20</gadget>
<output>64/5 = around 12.8</output>
<gadget id="calculator">(64/5) * 2</gadget>
<output>128/5 = around 25.6</output>
<gadget id="calculator">(128/5) + 20</gadget>
<output>228/5 = around 45.6</output>
<result>228/5 = around 45.6</result>


there are 180 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?

Explanation: "the number of nurses at the hospital is ( 3 / 5 ) * 180 = 108 . the answer is c ."

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">180 / 5</gadget>
<output>36</output>
<gadget id="calculator">36 * 3</gadget>
<output>108</output>
<result>108</result>


a reduction of 40 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?

Explanation: "800 * ( 40 / 100 ) = 320 - - - - 5 ? - - - - 1 = > rs . 64 answer : c"

divide(divide(multiply(800, 40), const_100), 5)

<gadget id="calculator">800 * 40</gadget>
<output>32_000</output>
<gadget id="calculator">32_000 / 100</gadget>
<output>320</output>
<gadget id="calculator">320 / 5</gadget>
<output>64</output>
<result>64</result>


what is the max number of rectangular boxes , each measuring 4 inches by 6 inches by 10 inches , that can be packed into a rectangular packing box measuring 16 inches by 18 inches by 30 inches , if all boxes are aligned in the same direction ?

Explanation: the 4 inch side should be aligned to the 16 inch side ( 4 layer ) 6 inch side should be aligned to the 18 inch side . ( 3 layer ) and 10 inch side should be aligned to the 30 inch side . ( 3 layer ) maximum number of rectangles = 4 * 3 * 3 = 36 answer is a

divide(multiply(multiply(16, 18), 30), multiply(multiply(4, 6), 10))

<gadget id="calculator">16 * 18</gadget>
<output>288</output>
<gadget id="calculator">288 * 30</gadget>
<output>8_640</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<gadget id="calculator">24 * 10</gadget>
<output>240</output>
<gadget id="calculator">8_640 / 240</gadget>
<output>36</output>
<result>36</result>


after decreasing 80 % in the price of an article costs rs . 320 . find the actual cost of an article ?

Explanation: "cp * ( 20 / 100 ) = 320 cp = 16 * 100 = > cp = 1600 answer : e"

divide(320, subtract(const_1, divide(80, const_100)))

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">320 / (1/5)</gadget>
<output>1_600</output>
<result>1_600</result>


a batsman had a certain average of runs for 16 innings . in the 17 th innings , he made a score of 87 runs thereby increasing his average by 3 . what is his average after 17 innings ?

Explanation: explanation : assume his initial average = xx his total runs after 16 innings = 16 xx after scoring 87 runs his average got increased by 3 to xx + 3 so his total runs after 17 innings = 17 × ( xx + 3 ) but it was given that the difference in the total scores after 16 innings and 17 innings = 87 therefore 17 × ( x + 3 ) − 16 x = 87 ⇒ x = 3617 × ( x + 3 ) − 16 x = 87 ⇒ x = 36 his new average = 36 + 3 = 39 answer : a

<gadget id="calculator">17 * 3</gadget>
<output>51</output>
<gadget id="calculator">87 - 51</gadget>
<output>36</output>
<gadget id="calculator">36 + 3</gadget>
<output>39</output>
<result>39</result>


if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is - .

Explanation: "explanation : p ( s ᴜ k ) = p ( s ) + p ( k ) - p ( s ∩ k ) , where s denotes spade and k denotes king . p ( s ᴜ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : b"

add(divide(const_3, const_52), divide(divide(const_52, const_4), const_52))

<gadget id="calculator">3 / 52</gadget>
<output>3/52 = around 0.057692</output>
<gadget id="calculator">52 / 4</gadget>
<output>13</output>
<gadget id="calculator">13 / 52</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(3/52) + (1/4)</gadget>
<output>4/13 = around 0.307692</output>
<result>4/13 = around 0.307692</result>


a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 5 % his yearly income diminishes by rs . 61.50 . his capital is

Explanation: explanation : capital = rs . x , then 4 / 5 x = 61.5 x = 76.88 answer : c ) rs . 76.88

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">61.5 / (4/5)</gadget>
<output>76.875</output>
<result>76.875</result>


thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 19 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?

Explanation: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 19 = 49 members have not passed the test , thus 0.7 * total = 49 - - > total = 70 . answer : b ."

divide(add(19, 30), divide(subtract(const_100, 30), const_100))

<gadget id="calculator">19 + 30</gadget>
<output>49</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">49 / (7/10)</gadget>
<output>70</output>
<result>70</result>


the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 14 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .

Explanation: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 14 = 406 hence , new average = 406 ⁄ 10 = 40.6 answer c"

<gadget id="calculator">40.2 * 10</gadget>
<output>402</output>
<gadget id="calculator">13 + 14</gadget>
<output>27</output>
<gadget id="calculator">402 + 27</gadget>
<output>429</output>
<gadget id="calculator">429 - 31</gadget>
<output>398</output>
<gadget id="calculator">398 / 10</gadget>
<output>199/5 = around 39.8</output>
<result>199/5 = around 39.8</result>


in 1990 the budgets for projects q and v were $ 500,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?

Explanation: "let the no of years it takes is x . 500 + 30 x = 780 - 10 x - - > 40 x = 280 and x = 7 . thus , it happens in 1997 . e ."

add(1990, multiply(10, multiply(const_2, const_3)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">10 * 6</gadget>
<output>60</output>
<gadget id="calculator">1_990 + 60</gadget>
<output>2_050</output>
<result>2_050</result>


how many numbers between 100 and 798 are divisible by 2 , 3 , and 7 together ?

Explanation: explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 798 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 798 : 798 / 42 = 19 hence , 42 * 19 = 798 is the last number divisible by 42 within 798 hence , total numbers divisible by 2 , 3 , 7 together are ( 19 â € “ 2 ) = 17 answer : d

subtract(divide(798, multiply(multiply(2, 3), 7)), divide(100, multiply(multiply(2, 3), 7)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">798 / 42</gadget>
<output>19</output>
<gadget id="calculator">100 / 42</gadget>
<output>50/21 = around 2.380952</output>
<gadget id="calculator">19 - (50/21)</gadget>
<output>349/21 = around 16.619048</output>
<result>349/21 = around 16.619048</result>


a car traveled 340 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 6 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?

Explanation: "let the speed in highway be h mpg and in city be c mpg . h = c + 6 h miles are covered in 1 gallon 340 miles will be covered in 340 / h . similarly c miles are covered in 1 gallon 336 miles will be covered in 336 / c . both should be same ( as car ' s fuel capacity does not change with speed ) = > 336 / c = 340 / h = > 336 / c = 340 / ( c + 6 ) = > 336 c + 336 * 6 = 340 c = > c = 336 * 6 / 4 = 504 answer a ."

divide(336, divide(subtract(340, 336), 6))

<gadget id="calculator">340 - 336</gadget>
<output>4</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">336 / (2/3)</gadget>
<output>504</output>
<result>504</result>


1850 men have provisions for 15 days . if 150 more men join them , for how many days will the provisions last now ?

Explanation: "1850 * 15 = 2000 * x x = 13.9 answer : c"

<gadget id="calculator">15 * 1_850</gadget>
<output>27_750</output>
<gadget id="calculator">1_850 + 150</gadget>
<output>2_000</output>
<gadget id="calculator">27_750 / 2_000</gadget>
<output>111/8 = around 13.875</output>
<result>111/8 = around 13.875</result>


a number increased by 30 % gives 780 . the number is

Explanation: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 30 % = 130 % 130 % - - - - - - - > 780 ( 130 × 6 = 780 ) 100 % - - - - - - - > 600 ( 100 × 6 = 600 ) d )"

divide(780, add(const_1, divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">780 / (13/10)</gadget>
<output>600</output>
<result>600</result>


if a > x > y > z on the number line , y is halfway between x and z , and x is halfway between w and z , then ( y - x ) / ( y - a ) =

Explanation: let y - z = t - - - > since y is halfway between x and z and x > y we have x - y = t . moreover x - z = ( x - y ) + ( y - z ) = 2 t . similarly since x is halfway between w and z , we have a - x = 2 t . so y - x = - t , y - a = - 3 t . - - - > ( y - x ) / ( y - a ) = 1 / 3 . the answer is ( b ) .

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

<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


3 friends james , david and charlie divide $ 1230 amongs them in such a way that if $ 5 , $ 10 and $ 15 are removed from the sums that james , david and charlie received respectively , then the share of the sums that they got will be in the ratio of 9 : 10 : 11 . how much did charlie receive ?

Explanation: a + b + c = 1230 given ratio 9 : 10 : 11 let us say the shares of a , b , c deducting 5 , 1015 be a , b , c a + b + c = 1230 - 30 = 1200 = 30 k c share = ( 1200 x 30 ) / 60 = 600 c = charlie share = 600 + 15 = 615 option e

<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">15 + 15</gadget>
<output>30</output>
<gadget id="calculator">1_230 - 30</gadget>
<output>1_200</output>
<gadget id="calculator">9 + 10</gadget>
<output>19</output>
<gadget id="calculator">19 + 11</gadget>
<output>30</output>
<gadget id="calculator">1_200 / 30</gadget>
<output>40</output>
<gadget id="calculator">11 * 40</gadget>
<output>440</output>
<gadget id="calculator">440 + 15</gadget>
<output>455</output>
<gadget id="calculator">455 + 40</gadget>
<output>495</output>
<gadget id="calculator">495 + 40</gadget>
<output>535</output>
<gadget id="calculator">535 + 40</gadget>
<output>575</output>
<gadget id="calculator">575 + 40</gadget>
<output>615</output>
<result>615</result>


a rectangular grass field is 70 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?

Explanation: "area = ( l + b + 2 d ) 2 d = ( 70 + 55 + 2.5 * 2 ) 2 * 2.5 = > 650 650 * 2 = rs . 1300 answer : b"

multiply(subtract(rectangle_area(add(70, multiply(2.5, 2)), add(55, multiply(2.5, 2))), rectangle_area(70, 55)), 2)

<gadget id="calculator">2.5 * 2</gadget>
<output>5</output>
<gadget id="calculator">70 + 5</gadget>
<output>75</output>
<gadget id="calculator">55 + 5</gadget>
<output>60</output>
<gadget id="calculator">75 * 60</gadget>
<output>4_500</output>
<gadget id="calculator">70 * 55</gadget>
<output>3_850</output>
<gadget id="calculator">4_500 - 3_850</gadget>
<output>650</output>
<gadget id="calculator">650 * 2</gadget>
<output>1_300</output>
<result>1_300</result>


calculate the area of a triangle , if the sides of are 39 cm , 36 cm and 15 cm , what is its area ?

Explanation: "the triangle with sides 39 cm , 36 cm and 15 is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 36 * 15 = 270 cm 2 answer : e"

<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 * 15</gadget>
<output>270</output>
<result>270</result>


a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 20 km in 20 hours . how much time he would have saved if the direction of tide has not changed ?

Explanation: "explanation : he covered 5 km in 1 hour , so he might cover 20 km in 4 hours . but he took 20 hours . he would have saved 20 â € “ 4 = 16 hours . answer : e"

<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">20 - 4</gadget>
<output>16</output>
<result>16</result>


a man can do a job in 15 days . his father takes 20 days and his son finishes it in 15 days . how long will they take to complete the job if they all work together ?

Explanation: "1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 15 ) = 11 / 60 so , all three together will complete the work in 300 / 47 = 5.5 days . answer : c"

divide(const_1, add(divide(const_1, 15), add(divide(const_1, 15), divide(const_1, 20))))

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(1/15) + (7/60)</gadget>
<output>11/60 = around 0.183333</output>
<gadget id="calculator">1 / (11/60)</gadget>
<output>60/11 = around 5.454545</output>
<result>60/11 = around 5.454545</result>


how long does a train 250 meters long running at the rate of 72 km / hr take to cross a bridge 150 meters in length ?

Explanation: "distance = length of train + length of bridge = 250 + 150 = 400 speed = 72 km / hr = 72 * 5 / 18 = 20 m / s required time = 400 / 20 = 20 seconds answer is b"

<gadget id="calculator">250 + 150</gadget>
<output>400</output>
<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">400 / 20</gadget>
<output>20</output>
<result>20</result>


the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 10 cents less than the price of commodity y ?

Explanation: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 10 cents less than commodity y . $ 2.00 / 25 cents = 8 years the answer is 2001 + 8 years = 2009 . the answer is b ."

add(2001, divide(add(divide(10, const_100), subtract(7.30, 5.20)), subtract(divide(45, const_100), subtract(7.30, 5.20))))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">7.3 - 5.2</gadget>
<output>2.1</output>
<gadget id="calculator">(1/10) + 2.1</gadget>
<output>2.2</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) - 2.1</gadget>
<output>-1.65</output>
<gadget id="calculator">2.2 / (-1.65)</gadget>
<output>-1.333333</output>
<gadget id="calculator">2_001 + (-1.333333)</gadget>
<output>1_999.666667</output>
<result>1_999.666667</result>


if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 , then find the total number of items the wholesaler distributes ?

Explanation: here , a : b : c : d = 1 / 12 : 1 / 13 : 1 / 15 : 1 / 2 1 ) l . c . m of 12 : 13 : 15 : 2 is 780 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 12 ) x 780 = 65 b = ( 1 / 13 ) x 780 = 60 c = ( 1 / 15 ) x 780 = 52 d = ( 1 / 2 ) x 780 = 390 3 ) total number of toys = ( 65 x + 60 x + 52 x + 390 x ) = 567 x minimum number of pens ( x ) = 1 therefore , total number of items = 567 items . correct option : a

add(add(multiply(const_100, const_4), const_100), add(multiply(15, const_4), add(const_4, const_3)))

<gadget id="calculator">100 * 4</gadget>
<output>400</output>
<gadget id="calculator">400 + 100</gadget>
<output>500</output>
<gadget id="calculator">15 * 4</gadget>
<output>60</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">60 + 7</gadget>
<output>67</output>
<gadget id="calculator">500 + 67</gadget>
<output>567</output>
<result>567</result>


john makes $ 50 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ?

Explanation: "increase = ( 10 / 50 ) * 100 = ( 1 / 5 ) * 100 = 20 % . e"

multiply(divide(subtract(60, 50), 50), const_100)

<gadget id="calculator">60 - 50</gadget>
<output>10</output>
<gadget id="calculator">10 / 50</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 90 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?

Explanation: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 90 % of 250 = 225 are boys who play soccer . girls who play soccer = 25 . total girls who do not play soccer = 108 - 25 = 83 . correct option : b"

subtract(subtract(420, 312), subtract(250, divide(multiply(250, 90), const_100)))

<gadget id="calculator">420 - 312</gadget>
<output>108</output>
<gadget id="calculator">250 * 90</gadget>
<output>22_500</output>
<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>
<gadget id="calculator">250 - 225</gadget>
<output>25</output>
<gadget id="calculator">108 - 25</gadget>
<output>83</output>
<result>83</result>


john bought a shirt on sale for 25 % off the original price and another 25 % off the discounted price . if the final price was $ 14 , what was the price before the first discount ?

Explanation: "let x be the price before the first discount . the price after the first discount is x - 25 % x ( price after first discount ) a second discount of 25 % of the discounted price after which the final price is 14 ( x - 25 % x ) - 25 % ( x - 25 % x ) = 14 solve for x x = $ 24.88 correct answer c"

divide(multiply(multiply(const_100, const_100), 14), subtract(multiply(subtract(const_100, 25), const_100), multiply(subtract(const_100, 25), 25)))

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * 14</gadget>
<output>140_000</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 * 100</gadget>
<output>7_500</output>
<gadget id="calculator">75 * 25</gadget>
<output>1_875</output>
<gadget id="calculator">7_500 - 1_875</gadget>
<output>5_625</output>
<gadget id="calculator">140_000 / 5_625</gadget>
<output>224/9 = around 24.888889</output>
<result>224/9 = around 24.888889</result>


the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1690 . the perimeter of the plot is ?

Explanation: "sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1650 x = 60 required perimeter = 2 ( 60 + 70 ) = 260 e"

multiply(add(divide(subtract(divide(divide(1690, 6.5), const_2), 10), const_2), add(divide(subtract(divide(divide(1690, 6.5), const_2), 10), const_2), 10)), const_2)

<gadget id="calculator">1_690 / 6.5</gadget>
<output>260</output>
<gadget id="calculator">260 / 2</gadget>
<output>130</output>
<gadget id="calculator">130 - 10</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<gadget id="calculator">60 + 70</gadget>
<output>130</output>
<gadget id="calculator">130 * 2</gadget>
<output>260</output>
<result>260</result>


the average weight of 4 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 95 kg . what might be the weight of the new person ?

Explanation: "total weight increased = ( 4 x 1.5 ) kg = 6 kg . weight of new person = ( 95 + 6 ) kg = 101 kg . answer : option a"

<gadget id="calculator">4 * 1.5</gadget>
<output>6</output>
<gadget id="calculator">6 + 95</gadget>
<output>101</output>
<result>101</result>


each of the three people individually can complete a certain job in 3 , 5 , and 6 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ?

Explanation: "the two slowest people work at rates of 1 / 5 and 1 / 6 of the job per hour . the sum of these rates is 1 / 5 + 1 / 6 = 11 / 30 of the job per hour . the answer is c ."

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/5) + (1/6)</gadget>
<output>11/30 = around 0.366667</output>
<result>11/30 = around 0.366667</result>


the average of 5 consecutive odd numbers a , b , c , d and e is 33 . what percent of a is d ?

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 33 and a = 31 and d = 35 required percentage = 31 / 35 x 100 = 88.6 answer : option b

multiply(const_100, divide(divide(multiply(33, 5), 5), add(add(add(divide(multiply(33, 5), 5), const_2), const_2), const_2)))

<gadget id="calculator">33 * 5</gadget>
<output>165</output>
<gadget id="calculator">165 / 5</gadget>
<output>33</output>
<gadget id="calculator">33 + 2</gadget>
<output>35</output>
<gadget id="calculator">35 + 2</gadget>
<output>37</output>
<gadget id="calculator">37 + 2</gadget>
<output>39</output>
<gadget id="calculator">33 / 39</gadget>
<output>11/13 = around 0.846154</output>
<gadget id="calculator">100 * (11/13)</gadget>
<output>1_100/13 = around 84.615385</output>
<result>1_100/13 = around 84.615385</result>


daniel went to a shop and bought things worth rs . 25 , out of which 60 paise went on sales tax on taxable purchases . if the tax rate was 6 % , then what was the cost of the tax free items ?

Explanation: "total cost of the items he purchased = rs . 25 given that out of this rs . 25 , 30 paise is given as tax = > total tax incurred = 60 paise = rs . 60 / 100 let the cost of the tax free items = x given that tax rate = 6 % ∴ ( 25 − 60 / 100 − x ) 6 / 100 = 60 / 100 ⇒ 6 ( 25 − 0.6 − x ) = 60 ⇒ ( 25 − 0.6 − x ) = 10 ⇒ x = 25 − 0.6 − 10 = 14.4 a"

subtract(subtract(25, divide(60, const_100)), divide(60, 6))

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">25 - (3/5)</gadget>
<output>122/5 = around 24.4</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<gadget id="calculator">(122/5) - 10</gadget>
<output>72/5 = around 14.4</output>
<result>72/5 = around 14.4</result>


the volumes of two cubes are in the ratio 27 : 125 , what shall be the ratio of their surface areas ?

Explanation: a 13 : a 23 = 27 : 125 a 1 : a 2 = 3 : 5 6 a 12 : 6 a 22 a 12 : a 22 = 9 : 25 answer : c

divide(surface_cube(divide(divide(27, const_3), const_3)), surface_cube(divide(125, divide(125, add(const_4, const_1)))))

<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<gadget id="calculator">6 * (3 ** 2)</gadget>
<output>54</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">125 / 5</gadget>
<output>25</output>
<gadget id="calculator">125 / 25</gadget>
<output>5</output>
<gadget id="calculator">6 * (5 ** 2)</gadget>
<output>150</output>
<gadget id="calculator">54 / 150</gadget>
<output>9/25 = around 0.36</output>
<result>9/25 = around 0.36</result>


bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .

Explanation: explanation : drawing two balls of same color from seven green balls can be done in â  · c â ‚ ‚ ways . similarly from eight white balls two can be drawn in â  ¸ c â ‚ ‚ ways . p = â  · c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ + â  ¸ c â ‚ ‚ / â ¹ â  µ c â ‚ ‚ = 7 / 15 a

divide(add(divide(factorial(7), multiply(factorial(subtract(7, const_2)), factorial(const_2))), divide(factorial(8), multiply(factorial(subtract(8, const_2)), factorial(const_2)))), divide(factorial(add(7, 8)), multiply(factorial(subtract(add(7, 8), const_2)), factorial(const_2))))

<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">120 * 2</gadget>
<output>240</output>
<gadget id="calculator">5_040 / 240</gadget>
<output>21</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">720 * 2</gadget>
<output>1_440</output>
<gadget id="calculator">40_320 / 1_440</gadget>
<output>28</output>
<gadget id="calculator">21 + 28</gadget>
<output>49</output>
<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">factorial(15)</gadget>
<output>1_307_674_368_000</output>
<gadget id="calculator">15 - 2</gadget>
<output>13</output>
<gadget id="calculator">factorial(13)</gadget>
<output>6_227_020_800</output>
<gadget id="calculator">6_227_020_800 * 2</gadget>
<output>12_454_041_600</output>
<gadget id="calculator">1_307_674_368_000 / 12_454_041_600</gadget>
<output>105</output>
<gadget id="calculator">49 / 105</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>


two trains of equal length , running with the speeds of 60 and 40 kmph , take 75 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?

Explanation: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 75 d = 75 * 100 / 18 = 1250 / 3 rs = 60 + 50 = 100 * 5 / 18 t = 1250 / 3 * 18 / 500 = 15 sec answer : a"

multiply(multiply(multiply(const_0_2778, subtract(60, 40)), 75), inverse(multiply(const_0_2778, add(60, 40))))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">(5/18) * 20</gadget>
<output>50/9 = around 5.555556</output>
<gadget id="calculator">(50/9) * 75</gadget>
<output>1_250/3 = around 416.666667</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">(5/18) * 100</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">1 / (250/9)</gadget>
<output>9/250 = around 0.036</output>
<gadget id="calculator">(1_250/3) * (9/250)</gadget>
<output>15</output>
<result>15</result>


if 40 % of a certain number is 160 , then what is 90 % of that number ?

Explanation: "explanation : 40 % = 40 * 4 = 160 90 % = 90 * 4 = 360 answer : option d"

multiply(divide(160, divide(40, const_100)), divide(90, const_100))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">160 / (2/5)</gadget>
<output>400</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">400 * (9/10)</gadget>
<output>360</output>
<result>360</result>


subtracting 30 from a number , the remainder is one fourth of the number . find the number ?

Explanation: explanation : 3 / 4 x = 30 = > x = 40 answer : c

divide(30, subtract(const_1, divide(const_1, const_4)))

<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">30 / (3/4)</gadget>
<output>40</output>
<result>40</result>


anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?

Explanation: "add the numbers of doughnuts . 12 + 6 + 8 = 26 . answer is b ."

<gadget id="calculator">12 + 6</gadget>
<output>18</output>
<gadget id="calculator">18 + 8</gadget>
<output>26</output>
<result>26</result>


in what time will a train 100 m long cross an electric pole , it its speed be 90 km / hr ?

Explanation: "speed = 90 * 5 / 18 = 25 m / sec time taken = 100 / 25 = 4 sec . answer : c"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">90 * (5/18)</gadget>
<output>25</output>
<gadget id="calculator">100 / 25</gadget>
<output>4</output>
<result>4</result>


if the number is divided by 3 , it reduced by 34 . the number is

Explanation: explanation : let the number be x . then , x - ( x / 3 ) = 34 = > 2 x / 3 = 34 = > x = 51 answer : option a

divide(multiply(34, 3), subtract(3, const_1))

<gadget id="calculator">34 * 3</gadget>
<output>102</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">102 / 2</gadget>
<output>51</output>
<result>51</result>


if a train runs at 40 kmph , it reach its destination late by 11 minutes but if it runs at 50 kmph it is late by 5 minutes only . the correct time for a train to complete its journey is ? let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min

Explanation: let the correct time to complete the journey be x min distance covered in ( x + 11 ) min . at 40 kmph distance covered in ( x + 5 ) min . at 50 kmph ( x + 11 ) / 60 * 40 = ( x + 5 ) / 60 * 50 x = 19 min answer ( a )

divide(subtract(multiply(multiply(60, 40), 11), multiply(multiply(60, 50), 5)), subtract(multiply(60, 50), multiply(60, 40)))

<gadget id="calculator">60 * 40</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 * 11</gadget>
<output>26_400</output>
<gadget id="calculator">60 * 50</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 * 5</gadget>
<output>15_000</output>
<gadget id="calculator">26_400 - 15_000</gadget>
<output>11_400</output>
<gadget id="calculator">3_000 - 2_400</gadget>
<output>600</output>
<gadget id="calculator">11_400 / 600</gadget>
<output>19</output>
<result>19</result>


share rs . 5400 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?

Explanation: "amount received by sanjay . 4 / 12 x 5400 = 1800 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1800 . a"

subtract(divide(5400, 2), divide(5400, 6))

<gadget id="calculator">5_400 / 2</gadget>
<output>2_700</output>
<gadget id="calculator">5_400 / 6</gadget>
<output>900</output>
<gadget id="calculator">2_700 - 900</gadget>
<output>1_800</output>
<result>1_800</result>