robert ' s salary was increased by 50 % and subsequently decreased by 10 % . how much percentage does he gain ?

Explanation: let original salary be $ 100 increased salary = 10 % of ( 150 % of $ 100 ) = ( 10 / 100 ) * ( 150 / 100 ) * 100 = $ 15 increase = 15 % correct option is a

subtract(subtract(multiply(multiply(divide(add(const_100, 50), const_100), divide(subtract(const_100, const_10), const_100)), const_100), const_100), multiply(10, const_2))

<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</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">(3/2) * (9/10)</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(27/20) * 100</gadget>
<output>135</output>
<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">35 - 20</gadget>
<output>15</output>
<result>15</result>


a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 29.16 , the number of the member is the group is :

Explanation: money collected = ( 29.16 x 100 ) paise = 29.16 paise numbers of members = 2916 squareroot = 54 answer b

<gadget id="calculator">29.16 * 100</gadget>
<output>2_916</output>
<gadget id="calculator">2_916 ** (1/2)</gadget>
<output>54</output>
<result>54</result>


a dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg , what is his percent ?

Explanation: "800 - - - 200 100 - - - ? = > 25 % answer : b"

subtract(multiply(divide(const_100, 800), multiply(const_100, multiply(add(const_3, const_2), const_2))), const_100)

<gadget id="calculator">100 / 800</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">(1/8) * 1_000</gadget>
<output>125</output>
<gadget id="calculator">125 - 100</gadget>
<output>25</output>
<result>25</result>


the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg . what might be the weight of the new person ?

Explanation: "c 86 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 66 + 20 ) kg = 86 kg ."

<gadget id="calculator">8 * 2.5</gadget>
<output>20</output>
<gadget id="calculator">20 + 66</gadget>
<output>86</output>
<result>86</result>


if ( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) , what is the value of x ?

Explanation: "( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) = > 5 ^ 9 * 3 ^ 10 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 9 * 3 ^ 10 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 9 answer b"

divide(log(divide(multiply(power(5, 9), power(9, 5)), 3)), log(15))

<gadget id="calculator">5 ** 9</gadget>
<output>1_953_125</output>
<gadget id="calculator">9 ** 5</gadget>
<output>59_049</output>
<gadget id="calculator">1_953_125 * 59_049</gadget>
<output>115_330_078_125</output>
<gadget id="calculator">115_330_078_125 / 3</gadget>
<output>38_443_359_375</output>
<gadget id="calculator">log(38_443_359_375)</gadget>
<output>log(38443359375) = around 24.372452</output>
<gadget id="calculator">log(15)</gadget>
<output>log(15) = around 2.70805</output>
<gadget id="calculator">log(38443359375) / log(15)</gadget>
<output>log(38443359375)/log(15) = around 9</output>
<result>log(38443359375)/log(15) = around 9</result>


a boat having a length 8 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "explanation : volume of water displaced = ( 8 x 2 x 0.01 ) m 3 = 0.16 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.16 x 1000 ) kg = 160 kg . answer : d"

multiply(multiply(multiply(8, 2), divide(1, const_100)), const_1000)

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">16 * (1/100)</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) * 1_000</gadget>
<output>160</output>
<result>160</result>


what is the sum between the place values of two 3 ' s in the numeral 63130

Explanation: required sum = 3000 + 30 = 3030 answer is d

add(multiply(3, const_10), multiply(3, const_1000))

<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">30 + 3_000</gadget>
<output>3_030</output>
<result>3_030</result>


lloyd normally works 7.5 hours per day and earns $ 4.00 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?

Explanation: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.0 + 3 * 4.0 * 1.5 = 48 answer b"

<gadget id="calculator">7.5 * 4</gadget>
<output>30</output>
<gadget id="calculator">10.5 - 7.5</gadget>
<output>3</output>
<gadget id="calculator">3 * 1.5</gadget>
<output>4.5</output>
<gadget id="calculator">4.5 * 4</gadget>
<output>18</output>
<gadget id="calculator">30 + 18</gadget>
<output>48</output>
<result>48</result>


the average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .

Explanation: "explanation : average weight of 20 boys = 50.25 total weight of 20 boys = 50.25 × 20 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 20 ) + ( 45.15 × 8 ) total boys = 20 + 8 = 28 average weight of all the boys = ( 50.25 × 20 ) + ( 45.15 × 8 ) / 28 = answer : option a"

<gadget id="calculator">20 * 50.25</gadget>
<output>1_005</output>
<gadget id="calculator">8 * 45.15</gadget>
<output>361.2</output>
<gadget id="calculator">1_005 + 361.2</gadget>
<output>1_366.2</output>
<gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">1_366.2 / 28</gadget>
<output>48.792857</output>
<result>48.792857</result>


what is the difference between the c . i . on rs . 9000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?

Explanation: c . i . when interest is compounded yearly = [ 9000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 9000 * 26 / 25 * 51 / 50 = rs . 9547.2 c . i . when interest is compounded half - yearly = [ 9000 * ( 1 + 2 / 100 ) 2 ] = ( 9000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 9550.87 difference = ( 9550.87 - 9547.2 ) = rs . 3.67 . answer : c

subtract(multiply(9000, multiply(multiply(add(const_1, divide(2, const_100)), add(const_1, divide(2, const_100))), add(const_1, divide(2, const_100)))), multiply(9000, multiply(add(const_1, divide(2, const_100)), add(const_1, divide(4, const_100)))))

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(51/50) * (51/50)</gadget>
<output>2_601/2_500 = around 1.0404</output>
<gadget id="calculator">(2_601/2_500) * (51/50)</gadget>
<output>132_651/125_000 = around 1.061208</output>
<gadget id="calculator">9_000 * (132_651/125_000)</gadget>
<output>1_193_859/125 = around 9_550.872</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(51/50) * (26/25)</gadget>
<output>663/625 = around 1.0608</output>
<gadget id="calculator">9_000 * (663/625)</gadget>
<output>47_736/5 = around 9_547.2</output>
<gadget id="calculator">(1_193_859/125) - (47_736/5)</gadget>
<output>459/125 = around 3.672</output>
<result>459/125 = around 3.672</result>


a tank is filled by 3 pipes a , b , c in 3 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?

Explanation: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 3 7 / x = 1 / 3 x = 21 hours answer is e"

multiply(add(add(multiply(const_2, const_2), const_2), const_1), 3)

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<result>21</result>


a girl multiplies 987 by a certain number and obtains 559981 as her answer . if in the answer , both 9 ’ s are wrong but the other digits are correct , then the correct answer will be

Explanation: 987 = 3 x 7 x 47 . so , required number must be divisible by each one of 3 , 7 , 47 . none of the numbers in 553681 and 555181 are divisible by 3 . while 556581 is not divisible by 7 . correct answer is 555681 . answer : c

add(subtract(559981, multiply(add(multiply(9, const_10), 9), const_100)), multiply(add(multiply(const_2, const_3), multiply(const_10, add(const_1, const_4))), const_100))

<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 + 9</gadget>
<output>99</output>
<gadget id="calculator">99 * 100</gadget>
<output>9_900</output>
<gadget id="calculator">559_981 - 9_900</gadget>
<output>550_081</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">6 + 50</gadget>
<output>56</output>
<gadget id="calculator">56 * 100</gadget>
<output>5_600</output>
<gadget id="calculator">550_081 + 5_600</gadget>
<output>555_681</output>
<result>555_681</result>


a couple spent $ 198 in total while dining out and paid this amount using a credit card . the $ 198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?

Explanation: let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 198 x = $ 150 the correct answer is c .

divide(multiply(divide(multiply(198, const_100), add(const_100, 20)), const_100), add(const_100, 10))

<gadget id="calculator">198 * 100</gadget>
<output>19_800</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">19_800 / 120</gadget>
<output>165</output>
<gadget id="calculator">165 * 100</gadget>
<output>16_500</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">16_500 / 110</gadget>
<output>150</output>
<result>150</result>


in an election , candidate douglas won 58 percent of the total vote in counties x and y . he won 64 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?

Explanation: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 64 % voted means 64 * 200 = 128 votes combined for xy has 300 voters and voted 58 % so total votes = 174 balance votes = 174 - 128 = 46 as y has 100 voters so 46 votes means 46 % of votes required ans e"

multiply(divide(subtract(divide(58, const_100), multiply(divide(64, const_100), divide(2, const_3))), divide(1, const_3)), const_100)

<gadget id="calculator">58 / 100</gadget>
<output>29/50 = around 0.58</output>
<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(16/25) * (2/3)</gadget>
<output>32/75 = around 0.426667</output>
<gadget id="calculator">(29/50) - (32/75)</gadget>
<output>23/150 = around 0.153333</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(23/150) / (1/3)</gadget>
<output>23/50 = around 0.46</output>
<gadget id="calculator">(23/50) * 100</gadget>
<output>46</output>
<result>46</result>


if x is an integer and 2.134 × 10 ^ x is less than 21,000 , what is the greatest possible value for x ?

Explanation: "x is an integer and 2.134 × 10 x is less than 21,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 21,000 to remain true , the greatest number is 2,134 , which makes x = 3 e . 3"

<gadget id="calculator">21_000 / 2.134</gadget>
<output>9_840.674789</output>
<gadget id="calculator">log(9_840.674789)</gadget>
<output>9.19428</output>
<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>
<gadget id="calculator">9.19428 / log(10)</gadget>
<output>9.19428/log(10) = around 3.993025</output>
<gadget id="calculator">floor(9.19428/log(10))</gadget>
<output>3</output>
<result>3</result>


a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? a . 480 liters

Explanation: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a

multiply(divide(multiply(24, 4), subtract(24, 20)), 20)

<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">24 - 20</gadget>
<output>4</output>
<gadget id="calculator">96 / 4</gadget>
<output>24</output>
<gadget id="calculator">24 * 20</gadget>
<output>480</output>
<result>480</result>


the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 78 kg and 93 kg join the group . find the initial number of members in the group ?

Explanation: let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 78 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 69 = > n = 23 therefore there were 23 members in the group initially . answer : c

divide(subtract(add(78, 93), multiply(51, const_2)), subtract(51, 48))

<gadget id="calculator">78 + 93</gadget>
<output>171</output>
<gadget id="calculator">51 * 2</gadget>
<output>102</output>
<gadget id="calculator">171 - 102</gadget>
<output>69</output>
<gadget id="calculator">51 - 48</gadget>
<output>3</output>
<gadget id="calculator">69 / 3</gadget>
<output>23</output>
<result>23</result>


Explanation: "answer 0.34 = 34 / 100 = 17 / 50 correct option : c"

divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 0.34), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">100 * 0.34</gadget>
<output>34</output>
<gadget id="calculator">34 / 100</gadget>
<output>17/50 = around 0.34</output>
<result>17/50 = around 0.34</result>


dhoni bought 5 toys with the average cost of $ 10 . if david also buys the sixth toy with the price of $ 16 , what is the average ( arithmetic mean ) price of those 6 toys ?

Explanation: 5 toys - > total cost = 5 * avg cost = 5 * 10 = 50 sixth toy cost = 16 total cost for 6 toys = 50 + 16 = 66 am = 66 / 6 = 11 hence e

<gadget id="calculator">10 + 12</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<result>11</result>


a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds . what is the length of the train in meters ?

Explanation: "relative speed of the train with respect to the motorbike should be the speed with which the length of the train is covered in 40 secs . calculate the relative speed = > 100 - 64 = 36 kmph and time is 40 sec = 40 / 3600 hrs distance ( in this case the length of the train ) = s * t = 36 * 40 / 3600 . 4 km or 400 meters . so answer ( a )"

multiply(multiply(subtract(100, 64), const_0_2778), 40)

<gadget id="calculator">100 - 64</gadget>
<output>36</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">10 * 40</gadget>
<output>400</output>
<result>400</result>


a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 350 m long platform ?

Explanation: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 350 ) / 36 * 5 / 18 = 47 min . answer : d"

divide(add(350, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">350 + 120</gadget>
<output>470</output>
<gadget id="calculator">470 / 10</gadget>
<output>47</output>
<result>47</result>


gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?

Explanation: "g = 10 w c = 6 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 6 wx = x + 1 * 8 w 10 + 6 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"

<gadget id="calculator">8 - 6</gadget>
<output>2</output>
<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<result>1</result>


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

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

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

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


a waitress ' s income consists of her salary and tips . during one week , her tips were 3 / 4 of her salary . what fraction of her income for the week came from tips ?

Explanation: "her tips were 3 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 3 / 4 ) ( $ 4 ) = $ 3 so , her total income = $ 4 + $ 3 = $ 7 what fraction of her income for the week came from tips $ 3 / $ 7 = 3 / 7 = c"

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>


the height of a triangle is decreased by 5 % and its base increased by 10 % . its area will

Explanation: explanation : let the initial height be 100 and the base be 200 units . â ˆ ´ area = 1 / 2 x 100 x 200 = 10000 sq units now , height = 95 units and base = 220 units â ˆ ´ new area = 1 / 2 x 95 x 220 = 10450 â ˆ ´ area is increased by ( 10450 - 10000 ) / 10000 x 10 = 4.5 % answer : option c

subtract(divide(multiply(subtract(const_100, 5), add(const_100, 10)), const_100), const_100)

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">95 * 110</gadget>
<output>10_450</output>
<gadget id="calculator">10_450 / 100</gadget>
<output>209/2 = around 104.5</output>
<gadget id="calculator">(209/2) - 100</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


the average age of 20 students of a class is 20 years . out of these , the average age of 9 students is 11 years and that of the other 10 students is 24 years . the age of the 20 th student is ?

Explanation: "age of the 20 th student = 20 * 20 - ( 9 * 11 + 10 * 24 ) = 400 - 339 = 61 years answer is b"

subtract(multiply(20, 20), add(multiply(9, 11), multiply(10, 24)))

<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">9 * 11</gadget>
<output>99</output>
<gadget id="calculator">10 * 24</gadget>
<output>240</output>
<gadget id="calculator">99 + 240</gadget>
<output>339</output>
<gadget id="calculator">400 - 339</gadget>
<output>61</output>
<result>61</result>


a man engaged a servant on the condition that he would pay him rs . 500 and a uniform after one year service . he served only for 9 months and received uniform and rs . 300 , find the price of the uniform ?

Explanation: "9 / 12 = 3 / 4 * 500 = 375 300 - - - - - - - - - - - - - 75 1 / 4 - - - - - - - - 75 1 - - - - - - - - - ? = > rs . 300 answer : d"

multiply(divide(subtract(multiply(9, 500), multiply(multiply(const_3, const_4), 300)), multiply(multiply(const_3, const_4), const_1)), const_4)

<gadget id="calculator">9 * 500</gadget>
<output>4_500</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 300</gadget>
<output>3_600</output>
<gadget id="calculator">4_500 - 3_600</gadget>
<output>900</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">900 / 12</gadget>
<output>75</output>
<gadget id="calculator">75 * 4</gadget>
<output>300</output>
<result>300</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 800 sq . ft , how many feet of fencing will be required ?

Explanation: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 800 = > breadth = 40 feet area to be fenced = 2 b + l = 2 * 40 + 20 = 100 feet answer : option a"

add(multiply(divide(800, 20), const_2), 20)

<gadget id="calculator">800 / 20</gadget>
<output>40</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">80 + 20</gadget>
<output>100</output>
<result>100</result>


every day daniel drives 60 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?

Explanation: "let ' s test x = 4 . . . . on sunday , daniel drove 60 miles at 4 miles / hour . d = ( r ) ( t ) 60 = ( 4 ) ( t ) 60 / 4 = 15 = t it takes 15 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 28 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 28 = ( 2 ) ( t ) 28 / 2 = 14 = t it takes 14 hours for the second part total time to drive home on monday = 4 + 14 = 18 hours we ' re asked by what percent 18 hours is greater than 15 hours . 18 / 15 = 1.2 , so it is 20 % greater . b"

multiply(divide(subtract(add(divide(32, 2), multiply(subtract(60, 32), 2)), 60), 60), const_100)

<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">60 - 32</gadget>
<output>28</output>
<gadget id="calculator">28 * 2</gadget>
<output>56</output>
<gadget id="calculator">16 + 56</gadget>
<output>72</output>
<gadget id="calculator">72 - 60</gadget>
<output>12</output>
<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


the length of a rectangle is halved , while its breadth is tripled . watis the % change in area ?

Explanation: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"

multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">3 * (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) - 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) / 1</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


the number of sailors on a ship is 85 % more than the number of officers . the ratio of sailors to officers would be

Explanation: "sailor = 1.85 * officer sailor / officer = 1.85 / 1 = 185 / 100 = 37 / 20 answer will be a"

<gadget id="calculator">85 + 100</gadget>
<output>185</output>
<gadget id="calculator">185 / 100</gadget>
<output>37/20 = around 1.85</output>
<result>37/20 = around 1.85</result>


a goods train runs at the speed of 72 km / hr and crosses a 270 m long platform in 26 sec . what is the length of the goods train ?

Explanation: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 270 ) / 26 = 20 x = 250 m . answer : d"

subtract(multiply(multiply(divide(72, const_3600), const_1000), 26), 270)

<gadget id="calculator">72 / 3_600</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) * 1_000</gadget>
<output>20</output>
<gadget id="calculator">20 * 26</gadget>
<output>520</output>
<gadget id="calculator">520 - 270</gadget>
<output>250</output>
<result>250</result>


the volume of water inside a swimming pool doubles every hour . if the pool is filled to its full capacity within 8 hours , in how many hours was it filled to one quarter of its capacity ?

<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<result>6</result>


there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure y in inches of the width of the foil covered prism ?

Explanation: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = y = 10 ans e ."

add(multiply(power(divide(128, multiply(1, multiply(1, const_2))), inverse(const_3)), multiply(1, const_2)), multiply(1, const_2))

<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">128 / 2</gadget>
<output>64</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<result>10</result>


a train 200 m long can cross an electric pole in 5 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 200 / 5 s = 40 m / sec speed = 40 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 144 kmph answer : d"

divide(divide(200, const_1000), divide(5, const_3600))

<gadget id="calculator">200 / 1_000</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">5 / 3_600</gadget>
<output>1/720 = around 0.001389</output>
<gadget id="calculator">(1/5) / (1/720)</gadget>
<output>144</output>
<result>144</result>


water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 1 / 9 meters . what is value of the radius in meters ?

Explanation: "10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 1 / 9 ) which is about 9 r = 3 the answer is b ."

<gadget id="calculator">10 * 0.31</gadget>
<output>3.1</output>
<gadget id="calculator">3.1 / 1</gadget>
<output>3.1</output>
<result>3.1</result>


a person crosses a 800 m long street in 5 minutes . what is his speed in km per hour ?

Explanation: "distance = 800 meter time = 5 minutes = 5 x 60 seconds = 300 seconds speed = distance / time = 800 / 300 = 2.67 m / s = 2.67 ã — 18 / 5 km / hr = 9.61 km / hr answer : e"

divide(divide(800, const_1000), divide(multiply(5, const_60), const_3600))

<gadget id="calculator">800 / 1_000</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">300 / 3_600</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(4/5) / (1/12)</gadget>
<output>48/5 = around 9.6</output>
<result>48/5 = around 9.6</result>


in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 15 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?

Explanation: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 15 m ahead . that means jhon was 15 m away from finishing line when they started together . so he will cover 15 m in 5 seconds . so his speed = 15 / 5 = 3 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 17 seconds . correct answer = e"

<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 5</gadget>
<output>17</output>
<result>17</result>


in an examination , 300 students appeared . out of these students ; 29 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .

Explanation: "the number of students with first division = 29 % of 300 = 29 / 100 × 300 = 8700 / 100 = 87 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 87 + 162 ) = 51 answer : a"

divide(multiply(300, subtract(const_100, add(29, 54))), const_100)

<gadget id="calculator">29 + 54</gadget>
<output>83</output>
<gadget id="calculator">100 - 83</gadget>
<output>17</output>
<gadget id="calculator">300 * 17</gadget>
<output>5_100</output>
<gadget id="calculator">5_100 / 100</gadget>
<output>51</output>
<result>51</result>


the length of rectangle is thrice its breadth and its perimeter is 104 m , find the area of the rectangle ?

Explanation: "2 ( 3 x + x ) = 104 l = 39 b = 13 lb = 39 * 13 = 507 answer : a"

multiply(multiply(divide(104, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(104, add(multiply(const_3, const_2), multiply(const_1, const_2))))

<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">104 / 8</gadget>
<output>13</output>
<gadget id="calculator">13 * 3</gadget>
<output>39</output>
<gadget id="calculator">39 * 13</gadget>
<output>507</output>
<result>507</result>


if x + y = 20 , x - y = 36 , for integers of x and y , x = ?

Explanation: "x + y = 20 x - y = 36 2 x = 56 x = 28 answer is c"

<gadget id="calculator">20 + 36</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 14 % , then the cost price of the article is :

Explanation: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 114 = rs . 540 answer : option b"

divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 14))

<gadget id="calculator">616 * 100</gadget>
<output>61_600</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">61_600 / 110</gadget>
<output>560</output>
<gadget id="calculator">560 * 110</gadget>
<output>61_600</output>
<gadget id="calculator">100 + 14</gadget>
<output>114</output>
<gadget id="calculator">61_600 / 114</gadget>
<output>30_800/57 = around 540.350877</output>
<result>30_800/57 = around 540.350877</result>


the speed of a boat in still water is 14 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 8 minutes is

Explanation: "explanation : speed downstreams = ( 14 + 5 ) kmph = 19 kmph . distance travelled = ( 19 x 8 / 60 ) km = 2.5 km option b"

multiply(divide(8, const_60), add(14, 5))

<gadget id="calculator">8 / 60</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">14 + 5</gadget>
<output>19</output>
<gadget id="calculator">(2/15) * 19</gadget>
<output>38/15 = around 2.533333</output>
<result>38/15 = around 2.533333</result>


Explanation: the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 19 has the form 5 n + 4 , so the tens digit of 6 ^ 19 is 9 . the answer is e .

floor(divide(reminder(power(6, reminder(19, add(const_4, const_1))), const_100), const_10))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">19 % 5</gadget>
<output>4</output>
<gadget id="calculator">6 ** 4</gadget>
<output>1_296</output>
<gadget id="calculator">1_296 % 100</gadget>
<output>96</output>
<gadget id="calculator">96 / 10</gadget>
<output>48/5 = around 9.6</output>
<gadget id="calculator">floor(48/5)</gadget>
<output>9</output>
<result>9</result>


aa is two digit number then m times its cube of aa has 1 in its tens place then what is m .

Explanation: when aa = 11 7 * ( 11 ) ^ 3 = 7 * 1331 = 9317 m = 7 answer : e

divide(multiply(power(add(const_10, 1), const_3), add(const_3, const_4)), power(add(const_10, 1), const_3))

<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 ** 3</gadget>
<output>1_331</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">1_331 * 7</gadget>
<output>9_317</output>
<gadget id="calculator">9_317 / 1_331</gadget>
<output>7</output>
<result>7</result>


a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability w that out of the two , one is white and one is blue ?

Explanation: "the required probability w = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."

divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2))

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">15 / 28</gadget>
<output>15/28 = around 0.535714</output>
<result>15/28 = around 0.535714</result>


the curved surface of a sphere is 64 π cm 2 . find its radius ?

Explanation: explanation : 4 π r 2 = 64 = > r = 4 answer : option c

<gadget id="calculator">64 / 4</gadget>
<output>16</output>
<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>
<result>4</result>


dhoni spent 25 percent of his earning last month on rent and 10 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?

Explanation: "say dhoni ' s earning last month was $ 100 . dhoni spent 30 percent of his earning last month on rent - - > $ 25 on rent ; 10 percent less than what he spent on rent to purchase a new dishwasher - - > $ 25 * 0.9 = $ 22.5 on the dishwasher . left over amount 100 - ( 25 + 22.5 ) = $ 52.5 answer : e"

subtract(const_100, add(25, multiply(25, subtract(const_1, divide(10, const_100)))))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">25 * (9/10)</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">25 + (45/2)</gadget>
<output>95/2 = around 47.5</output>
<gadget id="calculator">100 - (95/2)</gadget>
<output>105/2 = around 52.5</output>
<result>105/2 = around 52.5</result>


a present value of a machine is $ 800 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?

Explanation: "p = $ 800 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 800 * 9 / 10 * 9 / 10 = $ 648 answer is e"

multiply(800, power(subtract(const_1, divide(10, const_100)), 2))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>
<gadget id="calculator">800 * (81/100)</gadget>
<output>648</output>
<result>648</result>


the effective annual rate of interest corresponding to a nominal rate of 16 % per annum payable half - yearly is ?

Explanation: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 8 / 100 ) 2 ] = rs . 116.64 effective rate = ( 116.64 - 100 ) = 116.64 % answer : a"

add(add(divide(16, const_2), divide(16, const_2)), divide(multiply(divide(16, const_2), divide(16, const_2)), const_100))

<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 / 100</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">16 + (16/25)</gadget>
<output>416/25 = around 16.64</output>
<result>416/25 = around 16.64</result>


cost of 2 bats and 3 balls is rs . 1300 . the cost of 3 bats and 2 balls is rs . 1200 . the cost of each balls is more than that of each bat by ?

Explanation: 2 bats + 3 ball = 1300 - - - ( 1 ) 3 bats + 3 ball = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - bats + ball = 100 = > ball - bats = 100 b

<gadget id="calculator">1_300 - 1_200</gadget>
<output>100</output>
<result>100</result>


m = { - 6 , - 5 , - 4 , - 3 , - 2 } t = { - 2 , - 1 , 1 , 2 , 3 } if an integer is to be randomly selected from set m above and an integer is to be randomly selected from set t above , what is the probability that the product of the two integers will be negative ?

Explanation: answer e . total # of outcomes : 5 * 5 = 25 # of outcomes where product is - ve : ( - 6,1 ) , ( - 6,2 ) , ( - 6,3 ) . . . hence , total : 15 probability : 15 / 25 = 3 / 5

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


what is the total cost of 2 sandwiches at $ 2.45 each and 4 sodas at $ 0.87 each ?

Explanation: "answer = a 2 * 2.45 + 4 * 0.87 = 2 ( 2.50 - 0.05 ) + 4 ( 1.00 - 0.13 ) = 5 + 4 - 0.1 - 0.52 = 9 - 0.62 = 8.38"

add(multiply(2, 2.45), multiply(4, 0.87))

<gadget id="calculator">2 * 2.45</gadget>
<output>4.9</output>
<gadget id="calculator">4 * 0.87</gadget>
<output>3.48</output>
<gadget id="calculator">4.9 + 3.48</gadget>
<output>8.38</output>
<result>8.38</result>


a woman complete a journey in 5 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .

Explanation: "0.5 x / 21 + 0.5 x / 24 = 5 - - > x / 21 + x / 24 = 10 - - > x = 112 km . c"

multiply(multiply(divide(multiply(5, 24), add(24, 21)), 21), const_2)

<gadget id="calculator">5 * 24</gadget>
<output>120</output>
<gadget id="calculator">24 + 21</gadget>
<output>45</output>
<gadget id="calculator">120 / 45</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">(8/3) * 21</gadget>
<output>56</output>
<gadget id="calculator">56 * 2</gadget>
<output>112</output>
<result>112</result>


a rectangular field is to be fenced on three sides leaving a side of 34 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?

Explanation: "given that length and area , so we can find the breadth . length x breadth = area 34 x breadth = 680 breadth = 20 feet area to be fenced = 2 b + l = 2 ( 20 ) + 34 = 88 feet answer : a ) 74 ft"

add(multiply(divide(680, 34), const_2), 34)

<gadget id="calculator">680 / 34</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">40 + 34</gadget>
<output>74</output>
<result>74</result>


how many shots of 1 cm radius can be prepared from a sphere of 6 cm radius ?

Explanation: "4 / 3 ï € * 6 * 6 * 6 = 4 / 3 ï € * 1 * 1 * 1 * x x = 216 answer : c"

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">36 * 6</gadget>
<output>216</output>
<result>216</result>


a man can do a piece of work in 5 days , but with the help of his son , he can finish it in 4 days . in what time can the son do it alone ?

Explanation: "son ' s 1 day work = 1 / 4 - 1 / 5 = 1 / 20 son alone can do the work in 20 days = 20 days answer is e"

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">20 / 1</gadget>
<output>20</output>
<result>20</result>


a man & his wife appear in an interview for 2 vacancies in the same post . the probability of husband ' s selection is 1 / 7 & the probability of wife ' s selection is 1 / 5 . what is the probability that only 1 of them is selected ?

Explanation: let a = event that the husband is selected and b = event that the wife is selected . then , p ( a ) = 1 / 7 and p ( b ) = 1 / 5 ∴ p ( a ¯ ) = ( 1 - 17 / 5 ) = 6 / 7 and = ( 1 - 1 / 5 ) = 4 / 5 required probability = p [ ( a and not b ) or ( b and not a ) ] = p [ ( a and b ¯ ) or ( b and a ¯ ) ] = p ( a and b ¯ ) + p ( b and a ¯ ) = p ( a ) . p ( b ¯ ) + p ( b ) . p ( a ¯ ) = ( 1 / 7 * 4 / 5 ) + ( 1 / 5 * 6 / 7 ) = 10 / 35 = 2 / 7 c

add(multiply(divide(1, 5), subtract(1, divide(1, 7))), multiply(divide(1, 7), subtract(1, divide(1, 5))))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 - (1/7)</gadget>
<output>6/7 = around 0.857143</output>
<gadget id="calculator">(1/5) * (6/7)</gadget>
<output>6/35 = around 0.171429</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(1/7) * (4/5)</gadget>
<output>4/35 = around 0.114286</output>
<gadget id="calculator">(6/35) + (4/35)</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>


find the length of the wire required to go 11 times round a square field containing 27889 m 2 .

Explanation: "a 2 = 27889 = > a = 167 4 a = 668 668 * 11 = 7348 answer : a"

<gadget id="calculator">27_889 ** (1/2)</gadget>
<output>167</output>
<gadget id="calculator">4 * 167</gadget>
<output>668</output>
<gadget id="calculator">668 * 11</gadget>
<output>7_348</output>
<result>7_348</result>


there are 25 balls in a jar . you take out 5 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?

Explanation: "9 = 5 blue balls + 20 / 5 answer : b"

<gadget id="calculator">25 - 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 + 5</gadget>
<output>9</output>
<result>9</result>


a circular well with a diameter of 4 metres , is dug to a depth of 24 metres . what is the volume of the earth dug out ?

Explanation: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 24 ) m 3 ‹ = › 301.6 m 3 . answer e"

<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<gadget id="calculator">pi * (2 ** 2) * 24</gadget>
<output>96*pi = around 301.592895</output>
<result>96*pi = around 301.592895</result>


priya and her father differ in their ages by 31 years . after 8 years . if the sum of their ages will be 69 , their present ages are

Explanation: a 11 , 42 let the age of priya = x years then , the age of her father = ( x + 31 ) years atq , ( x + 8 ) + ( x + 31 + 8 ) = 69 2 x + 47 = 69 2 x = 69 – 47 = 22 x = 11 the age of priya = 11 years the age of her father = 11 + 31 = 42 years

subtract(divide(add(subtract(subtract(69, 8), 8), 31), const_2), 31)

<gadget id="calculator">69 - 8</gadget>
<output>61</output>
<gadget id="calculator">61 - 8</gadget>
<output>53</output>
<gadget id="calculator">53 + 31</gadget>
<output>84</output>
<gadget id="calculator">84 / 2</gadget>
<output>42</output>
<gadget id="calculator">42 - 31</gadget>
<output>11</output>
<result>11</result>


if 7 spiders make 7 webs in 7 days , then how many days are needed for 1 spider to make 1 web ?

Explanation: "explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 7 : 1 ( webs ) 1 : 7 } : : x : 7 ⇒ 7 × 1 × 7 = 1 × 7 × x ⇒ x = 7 answer : option b"

<gadget id="calculator">1 * 7</gadget>
<output>7</output>
<result>7</result>


the price of lunch for 13 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?

Explanation: "clearly c is the answer i used poe here lets consider option ( c ) 13 * 13.85 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo c"

divide(divide(multiply(207, subtract(const_100, 15)), const_100), 13)

<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">207 * 85</gadget>
<output>17_595</output>
<gadget id="calculator">17_595 / 100</gadget>
<output>3_519/20 = around 175.95</output>
<gadget id="calculator">(3_519/20) / 13</gadget>
<output>3_519/260 = around 13.534615</output>
<result>3_519/260 = around 13.534615</result>


find the principle on a certain sum of money at 5 % per annum for 2 years if the amount being rs . 1120 ?

Explanation: "1120 = p [ 1 + ( 5 * 2 ) / 100 ] p = 1018 answer : a"

divide(1120, add(const_1, divide(multiply(5, 2), const_100)))

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">1_120 / (11/10)</gadget>
<output>11_200/11 = around 1_018.181818</output>
<result>11_200/11 = around 1_018.181818</result>


a man swims downstream 24 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?

Explanation: "24 - - - 4 ds = 6 ? - - - - 1 16 - - - - 4 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"

divide(add(divide(16, 4), divide(24, 4)), const_2)

<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">24 / 4</gadget>
<output>6</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 38 , what is the remainder when k is divided by 7 ?

Explanation: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 , 27 , 32 , 37 } ( less than 38 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 , 29,35 } ( less than 38 ) 17 is the only common number in both the sets . hence k = 17 answer : c"

<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">17 % 7</gadget>
<output>3</output>
<result>3</result>


a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 6000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?

Explanation: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 6000 ) = rs . 750 answer = d"

multiply(multiply(subtract(inverse(3), add(inverse(8), inverse(6))), 6000), 3)

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/8) + (1/6)</gadget>
<output>7/24 = around 0.291667</output>
<gadget id="calculator">(1/3) - (7/24)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/24) * 6_000</gadget>
<output>250</output>
<gadget id="calculator">250 * 3</gadget>
<output>750</output>
<result>750</result>


if an organization were to sell n tickets for a theater production , the total revenue from ticket sales would be 20 percent greater than the total costs of the production . if the organization actually sold all but 5 percent of the n tickets , the total revenue from ticket sales was what percent greater than the total costs of the production ?

Explanation: let cost of prod for 1 ticket = 1 so cop for n tickets = n so for selling n tickets , sp = 1.2 * n = 1.2 n so sp of 1 ticket = 1.2 sp of 95 % tickets = 1.2 * 0.95 n so profit % = ( 1.2 * 0.95 n - n ) / n * 100 = 0.14 * 100 = 14 % answer - c

<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">16 - 2</gadget>
<output>14</output>
<result>14</result>


virginia , adrienne , and dennis have taught history for a combined total of 96 years . if virginia has taught for 9 more years than adrienne and for 12 fewer years than dennis , for how many years has dennis taught ?

Explanation: let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 12 = > a = ( d - 12 ) - 9 = d - 21 d - 9 + d - 21 + d = 96 = > 3 d = 96 + 30 = 126 = > d = 42 answer e

add(divide(subtract(96, add(add(9, 12), 9)), const_3), add(9, 12))

<gadget id="calculator">9 + 12</gadget>
<output>21</output>
<gadget id="calculator">21 + 9</gadget>
<output>30</output>
<gadget id="calculator">96 - 30</gadget>
<output>66</output>
<gadget id="calculator">66 / 3</gadget>
<output>22</output>
<gadget id="calculator">22 + 21</gadget>
<output>43</output>
<result>43</result>


an aeroplane covers a certain distance of 670 kmph in 6 hours . to cover the same distance in 6 1 / 4 hours , it must travel at a speed of

Explanation: "speed of aeroplane = 670 kmph distance travelled in 6 hours = 670 * 6 = 4020 km speed of aeroplane to acver 4020 km in 25 / 4 = 4020 * 4 / 25 = 643 km answer c ."

divide(multiply(670, 6), divide(add(multiply(4, 6), 1), 4))

<gadget id="calculator">670 * 6</gadget>
<output>4_020</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">25 / 4</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">4_020 / (25/4)</gadget>
<output>3_216/5 = around 643.2</output>
<result>3_216/5 = around 643.2</result>


a cube is divided into 216 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?

Explanation: each side of the cube has 6 x 6 = 36 cubelets . only the interior cubelets are painted one colour . on each side , 4 x 4 = 16 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 16 = 96 the answer is c .

divide(subtract(216, multiply(multiply(const_4, const_2), const_3)), const_2)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">216 - 24</gadget>
<output>192</output>
<gadget id="calculator">192 / 2</gadget>
<output>96</output>
<result>96</result>


a sum fetched a total simple interest of $ 4061.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

Explanation: "e 8926 principal = $ 100 x 4016.25 / 9 x 5 = $ 406125 / 45 = $ 8926 ."

divide(divide(multiply(4061.25, const_100), 9), 5)

<gadget id="calculator">4_061.25 * 100</gadget>
<output>406_125</output>
<gadget id="calculator">406_125 / 9</gadget>
<output>45_125</output>
<gadget id="calculator">45_125 / 5</gadget>
<output>9_025</output>
<result>9_025</result>


the average of 5 consecutive odd numbers is 55 . what is the difference between the highest and lowest numbers ?

Explanation: explanation : let the numbers be x , x + 2 , x + 4 , x + 6 and x + 8 . then , ( x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) ) / 5 = 55 5 x + 20 = 275 x = 255 / 5 = 51 . so , required difference = ( 51 + 8 ) 51 = 8 answer : c

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


in a class of 25 students in an examination in maths 3 students scored 95 marks each , 5 get zero each and the average of the rest was 45 . what is the average of the whole class ?

Explanation: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 5 * 0 + 17 * 45 = 1050 average marks of whole class = 1050 / 25 = 42 answer : option c"

divide(add(multiply(45, subtract(25, add(5, 3))), multiply(95, 3)), 25)

<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">25 - 8</gadget>
<output>17</output>
<gadget id="calculator">45 * 17</gadget>
<output>765</output>
<gadget id="calculator">95 * 3</gadget>
<output>285</output>
<gadget id="calculator">765 + 285</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 / 25</gadget>
<output>42</output>
<result>42</result>


a school has 4 section of chemistry in class x having 40 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .

Explanation: "required average marks = 40 × 50 + 35 × 60 + 45 × 55 + 42 × 45 / 40 + 35 + 45 + 42 = 2000 + 2100 + 2475 + 1890 / 162 = 8465 ⁄ 162 = 52.25 answer b"

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">35 * 60</gadget>
<output>2_100</output>
<gadget id="calculator">2_000 + 2_100</gadget>
<output>4_100</output>
<gadget id="calculator">45 * 55</gadget>
<output>2_475</output>
<gadget id="calculator">4_100 + 2_475</gadget>
<output>6_575</output>
<gadget id="calculator">42 * 45</gadget>
<output>1_890</output>
<gadget id="calculator">6_575 + 1_890</gadget>
<output>8_465</output>
<gadget id="calculator">40 + 35</gadget>
<output>75</output>
<gadget id="calculator">75 + 45</gadget>
<output>120</output>
<gadget id="calculator">120 + 42</gadget>
<output>162</output>
<gadget id="calculator">8_465 / 162</gadget>
<output>8_465/162 = around 52.253086</output>
<result>8_465/162 = around 52.253086</result>


ajay can walk 7 km in 1 hour . in how many hours he can walk 80 km ?

Explanation: "1 hour he walk 8 km he walk 80 km in = 80 / 7 * 1 = 11.4 hours answer is b"

<gadget id="calculator">80 / 7</gadget>
<output>80/7 = around 11.428571</output>
<result>80/7 = around 11.428571</result>


the percentage profit earned by selling an article for rs . 1320 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?

Explanation: "c . p . be rs . x . then , ( 1320 - x ) / x * 100 = ( x - 1280 ) / x * 100 1320 - x = x - 1280 2 x = 2600 = > x = 1300 required s . p . = 125 % of rs . 1300 = 125 / 100 * 1300 = rs . 1625 . anser d"

multiply(divide(add(const_100, 25), const_100), divide(add(1320, 1280), const_2))

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_320 + 1_280</gadget>
<output>2_600</output>
<gadget id="calculator">2_600 / 2</gadget>
<output>1_300</output>
<gadget id="calculator">(5/4) * 1_300</gadget>
<output>1_625</output>
<result>1_625</result>


130 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?

Explanation: "1 women ' s 1 day work = 1 / 910 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 910 + 10 / 140 ) = 1 / 13 5 women and 10 children will complete the work in 13 days . answer : e"

inverse(add(divide(5, multiply(130, 7)), divide(130, multiply(130, 14))))

<gadget id="calculator">130 * 7</gadget>
<output>910</output>
<gadget id="calculator">5 / 910</gadget>
<output>1/182 = around 0.005495</output>
<gadget id="calculator">130 * 14</gadget>
<output>1_820</output>
<gadget id="calculator">130 / 1_820</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/182) + (1/14)</gadget>
<output>1/13 = around 0.076923</output>
<gadget id="calculator">1 / (1/13)</gadget>
<output>13</output>
<result>13</result>


a grocer has a sale of rs . 3435 , rs . 3920 , rs . 3855 , rs . 4230 and rs . 3560 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?

Explanation: "total sale for 5 months = rs . ( 3435 + 3920 + 3855 + 4230 + 3560 ) = rs . 19000 . required sale = rs . [ ( 3500 x 6 ) - 19000 ] = rs . ( 21000 - 19000 ) = rs . 2000 answer : option e"

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 3_500</gadget>
<output>21_000</output>
<gadget id="calculator">3_435 + 3_920</gadget>
<output>7_355</output>
<gadget id="calculator">7_355 + 3_855</gadget>
<output>11_210</output>
<gadget id="calculator">11_210 + 4_230</gadget>
<output>15_440</output>
<gadget id="calculator">15_440 + 3_560</gadget>
<output>19_000</output>
<gadget id="calculator">21_000 - 19_000</gadget>
<output>2_000</output>
<result>2_000</result>


a number of 55 marbles is to be divided and contain with boxes . if each box is to contain 3 , 4 , or 5 marbles , what is the largest possible number of boxes ?

Explanation: to maximize # of boxes we should minimize marbles per box : 17 * 3 + 1 * 4 + 1 * 5 = 50 - - > 17 + 1 + 1 = 19 . answer : e .

<gadget id="calculator">55 / 3</gadget>
<output>55/3 = around 18.333333</output>
<result>55/3 = around 18.333333</result>


the length of a side of a hexagon is 7 inches . what is the perimeter ?

Explanation: "hexagon . it means 6 equal sides . p = 6 ( 7 ) = 42 inches answer b"

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">7 * 6</gadget>
<output>42</output>
<result>42</result>


how many numbers from 45 to 110 are exactly divisible by 12 ?

Explanation: "option ' c ' 45 / 12 = 3 and 110 / 12 = 9 = = > 9 - 3 = 6 numbers"

add(divide(subtract(multiply(floor(divide(110, 12)), 12), multiply(add(floor(divide(45, 12)), const_1), 12)), 12), const_1)

<gadget id="calculator">110 / 12</gadget>
<output>55/6 = around 9.166667</output>
<gadget id="calculator">floor(55/6)</gadget>
<output>9</output>
<gadget id="calculator">9 * 12</gadget>
<output>108</output>
<gadget id="calculator">45 / 12</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">floor(15/4)</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<gadget id="calculator">108 - 48</gadget>
<output>60</output>
<gadget id="calculator">60 / 12</gadget>
<output>5</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<result>6</result>


40 is subtracted from 60 % of a number , the result is 50 . find the number ?

Explanation: "( 60 / 100 ) * x – 40 = 50 6 x = 900 x = 150 answer : a"

divide(add(40, 50), divide(60, const_100))

<gadget id="calculator">40 + 50</gadget>
<output>90</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">90 / (3/5)</gadget>
<output>150</output>
<result>150</result>


a man has rs . 10350 in the form of rs . 50 notes and rs . 500 notes . the total number of notes are 108 . find the number of notes of rs . 50 denomination .

Explanation: "total money = rs . 10350 . let 50 rupees note was x . then 500 rupees note = 108 - x now , 50 * x + 500 * ( 108 - x ) = 10350 50 x + 54000 - 500 x = 10350 - 450 x = - 43650 x = 97 . no . of 50 rupees note = 97 . answer : option e"

divide(subtract(multiply(500, 108), 10350), subtract(500, 50))

<gadget id="calculator">500 * 108</gadget>
<output>54_000</output>
<gadget id="calculator">54_000 - 10_350</gadget>
<output>43_650</output>
<gadget id="calculator">500 - 50</gadget>
<output>450</output>
<gadget id="calculator">43_650 / 450</gadget>
<output>97</output>
<result>97</result>


a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day 5 miles per hour for 6 hours . how many miles in total did she walk ?

Explanation: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 5 miles per hour and 6 hours - 30 miles total 18 + 20 + 30 = 68 answer : option a .

add(add(18, multiply(5, const_4)), multiply(5, 6))

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">38 + 30</gadget>
<output>68</output>
<result>68</result>


after a storm deposits 120 billion gallons of water into the city reservoir , the reservoir is 85 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?

Explanation: "when the storm deposited 120 billion gallons , volume of water in the reservoir = 220 + 120 = 340 billion gallons if this is only 85 % of the capacity of the reservoir , the total capacity of the reservoir = 340 / 0.85 = 400 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 400 ) * 100 = 55 % option c"

multiply(divide(220, divide(add(120, 220), divide(85, const_100))), const_100)

<gadget id="calculator">120 + 220</gadget>
<output>340</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">340 / (17/20)</gadget>
<output>400</output>
<gadget id="calculator">220 / 400</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">(11/20) * 100</gadget>
<output>55</output>
<result>55</result>


Explanation: "72518 x 9999 = 72517 x ( 10000 - 1 ) = 72517 x 10000 - 72517 x 1 = 725170000 - 72517 = 725097483 d"

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 72_517</gadget>
<output>724_807_415</output>
<result>724_807_415</result>


10 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2907 , how much was it in the beginning ?

Explanation: "x * ( 90 / 100 ) * ( 85 / 100 ) = 2907 x = 3800 answer : a"

floor(divide(2907, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 15), const_100))))

<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 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(9/10) * (17/20)</gadget>
<output>153/200 = around 0.765</output>
<gadget id="calculator">2_907 / (153/200)</gadget>
<output>3_800</output>
<gadget id="calculator">floor(3_800)</gadget>
<output>3_800</output>
<result>3_800</result>


average of 5 numbers is 20 , and the sum of 3 of the numbers is 48 , what is the average of the other 2 numbers ?

Explanation: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e ) / 5 = 20 a + b + c = 48 ( 48 + d + e ) / 5 = 20 48 + d + e = 100 d + e = 52 average = 52 / 2 = 26 ans e

divide(subtract(multiply(20, 5), 48), 2)

<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">100 - 48</gadget>
<output>52</output>
<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>26</result>


the population of a city increases by 4 % per year but due to migration it decrease by 1 % per years . what will be the percentage increase in population in 3 years ?

Explanation: "actual increase in population = 3 % let , earlier population = 100 then the population after 3 years = 100 ( 1 + 3 / 100 ) ^ 3 = 109.2727 ∴ required percentage = 9.27 % answer : b"

add(divide(multiply(add(const_100, add(divide(multiply(add(const_100, subtract(4, 1)), subtract(4, 1)), const_100), subtract(4, 1))), subtract(4, 1)), const_100), add(divide(multiply(add(const_100, subtract(4, 1)), subtract(4, 1)), const_100), subtract(4, 1)))

<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">100 + 3</gadget>
<output>103</output>
<gadget id="calculator">103 * 3</gadget>
<output>309</output>
<gadget id="calculator">309 / 100</gadget>
<output>309/100 = around 3.09</output>
<gadget id="calculator">(309/100) + 3</gadget>
<output>609/100 = around 6.09</output>
<gadget id="calculator">100 + (609/100)</gadget>
<output>10_609/100 = around 106.09</output>
<gadget id="calculator">(10_609/100) * 3</gadget>
<output>31_827/100 = around 318.27</output>
<gadget id="calculator">(31_827/100) / 100</gadget>
<output>31_827/10_000 = around 3.1827</output>
<gadget id="calculator">(31_827/10_000) + (609/100)</gadget>
<output>92_727/10_000 = around 9.2727</output>
<result>92_727/10_000 = around 9.2727</result>


a rectangle measures 8 cm on length and its diagonal measures 17 cm . what is the perimeter of the rectangle ?

Explanation: second side = √ 17 power 2 - 8 power 2 = √ 289 - 64 = 15 cm perimeter = 2 ( l + b ) = 2 ( 8 + 5 ) cm = 2 ( 23 ) = 46 cm answer is c .

rectangle_perimeter(sqrt(subtract(power(17, const_2), power(8, const_2))), 8)

<gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">289 - 64</gadget>
<output>225</output>
<gadget id="calculator">225 ** (1/2)</gadget>
<output>15</output>
<gadget id="calculator">2 * (15 + 8)</gadget>
<output>46</output>
<result>46</result>


a train running at the speed of 48 km / hr crosses a pole in 9 seconds . what is the length of the train ?

Explanation: "speed = ( 48 x 5 / 18 ) m / sec = ( 40 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( 40 / 3 x 9 ) m = 120 m . answer is c ."

multiply(divide(multiply(48, const_1000), const_3600), 9)

<gadget id="calculator">48 * 1_000</gadget>
<output>48_000</output>
<gadget id="calculator">48_000 / 3_600</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">(40/3) * 9</gadget>
<output>120</output>
<result>120</result>


the average height of 35 boys in a class was calculated as 185 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?

Explanation: "calculated average height of 35 boys = 185 cm . wrong total height of 35 boys = 185 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 185 cm - ( 166 cm - 106 cm ) / 35 = 185 cm - 60 / 35 cm = 185 cm - 1.71 cm = 183.29 cm . answer : b"

floor(divide(add(subtract(multiply(35, 185), 166), 106), 35))

<gadget id="calculator">35 * 185</gadget>
<output>6_475</output>
<gadget id="calculator">6_475 - 166</gadget>
<output>6_309</output>
<gadget id="calculator">6_309 + 106</gadget>
<output>6_415</output>
<gadget id="calculator">6_415 / 35</gadget>
<output>1_283/7 = around 183.285714</output>
<gadget id="calculator">floor(1_283/7)</gadget>
<output>183</output>
<result>183</result>


the cost to park a car in a certain parking garage is $ 10.00 for up to 2 hours of parking and $ 1.75 for each hour in excess of 2 hours . what is the average ( arithmetic mean ) cost per hour to park a car in the parking garage for 9 hours ?

Explanation: "total cost of parking for 10 hours = 10 $ for the first 2 hours and then 1.75 for ( 9 - 2 ) hours = 10 + 7 * 1.75 = 22.25 thus the average parking price = 22.25 / 9 = 2.47 $ d is the correct answer ."

divide(add(10.00, multiply(1.75, subtract(9, 2))), 9)

<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">1.75 * 7</gadget>
<output>12.25</output>
<gadget id="calculator">10 + 12.25</gadget>
<output>22.25</output>
<gadget id="calculator">22.25 / 9</gadget>
<output>2.472222</output>
<result>2.472222</result>


at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 205 ?

Explanation: "i think it should be c . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 7 20 - pack for 3.05 * 7 = $ 21.35 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 7 = 2140"

<gadget id="calculator">205 / 22.95</gadget>
<output>8.932462</output>
<gadget id="calculator">8.932462 * 250</gadget>
<output>2_233.1155</output>
<result>2_233.1155</result>


a man can row upstream at 25 kmph and downstream at 45 kmph , and then find the speed of the man in still water ?

Explanation: "us = 25 ds = 45 m = ( 45 + 25 ) / 2 = 35 answer : e"

<gadget id="calculator">25 + 45</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>


the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :

Explanation: "explanation : l . c . m . of 5 , 6 , 7 , 8 = 840 . { \ color { blue } \ therefore } required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . { \ color { blue } \ therefore } required number = ( 840 x 2 + 3 ) = 1683 . answer : b ) 1683"

multiply(lcm(lcm(lcm(5, 6), 7), 8), const_2)

<gadget id="calculator">lcm(5, 6)</gadget>
<output>30</output>
<gadget id="calculator">lcm(30, 7)</gadget>
<output>210</output>
<gadget id="calculator">lcm(210, 8)</gadget>
<output>840</output>
<gadget id="calculator">840 * 2</gadget>
<output>1_680</output>
<result>1_680</result>


1 men takes 37 $ to eat a pizza in restaurant such that it have discount multiple of 4 if u eat more pizza . discount increase by multiple of 4 every pizza u eat . for 1 pizza 0 % off . for 2 pizza % off for 3 pizza 8 % off . pizza without discount is 10 $ . how much that man eats the pizza .

Explanation: solution : b . for 1 pizza 10 $ . for 2 pizza 10 $ + 9.6 $ ( 4 % off ) = 19.6 , for 3 pizza 19.6 + 9.2 ( 8 % off ) = 28.8 , for 4 pizza 28.8 + 8.8 ( 12 % off ) = 37.6 . so he have 37 so he cant eat 4 th pizza .

<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">40 - 37</gadget>
<output>3</output>
<result>3</result>


if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 46 ?

Explanation: "four wheeler = 11 * 4 = 44 ( max ) 2 wheel = 1 so no of 4 wheeler = 11 answer : a"

<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">44 / 4</gadget>
<output>11</output>
<result>11</result>


a train 250 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?

Explanation: "d = 72 * 5 / 18 = 25 = 500 – 250 = 250 m answer : c"

subtract(multiply(25, multiply(72, const_0_2778)), 250)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">25 * 20</gadget>
<output>500</output>
<gadget id="calculator">500 - 250</gadget>
<output>250</output>
<result>250</result>


a 9 % stock yields 8 % . the market value of the stock is :

Explanation: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 9 , investment = rs . ( 100 / 8 x 9 ) = rs . 112.50 ∴ market value of rs . 100 stock = rs . 112.50 answer c"

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 9</gadget>
<output>225/2 = around 112.5</output>
<result>225/2 = around 112.5</result>


one side of a rectangular field is 15 m and one of its diagonal is 18 m . find the area of the field .

Explanation: "solution other side = √ ( 18 ) 2 - ( 15 ) 2 = √ 324 - 225 = √ 99 = 9.9 m . ∴ area = ( 15 x 9.9 ) m 2 = 148.5 m 2 . answer d"

rectangle_area(15, sqrt(subtract(power(18, const_2), power(15, const_2))))

<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">324 - 225</gadget>
<output>99</output>
<gadget id="calculator">99 ** (1/2)</gadget>
<output>3*sqrt(11) = around 9.949874</output>
<gadget id="calculator">15 * (3*sqrt(11))</gadget>
<output>45*sqrt(11) = around 149.248116</output>
<result>45*sqrt(11) = around 149.248116</result>


the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 40 , what is the possible maximum range of the temperatures ?

Explanation: "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 40 , max would be 300 - 4 * 40 = 140 - - > the range = 140 ( max ) - 40 ( min ) = 100 answer : a"

subtract(subtract(multiply(60, add(const_2, const_3)), multiply(40, const_4)), 40)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">60 * 5</gadget>
<output>300</output>
<gadget id="calculator">40 * 4</gadget>
<output>160</output>
<gadget id="calculator">300 - 160</gadget>
<output>140</output>
<gadget id="calculator">140 - 40</gadget>
<output>100</output>
<result>100</result>


find out the square of a number which when doubled exceeds its one sixth by 11 ?

Explanation: "a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 6 ) + 11 = > 12 p = p + 66 = > p = 6 p ^ 2 = 6 ^ 2 = 36 . answer : a"

power(divide(11, subtract(const_2, divide(const_1, add(const_4, const_1)))), const_2)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">2 - (1/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">11 / (9/5)</gadget>
<output>55/9 = around 6.111111</output>
<gadget id="calculator">(55/9) ** 2</gadget>
<output>3_025/81 = around 37.345679</output>
<result>3_025/81 = around 37.345679</result>


a train overtakes two persons who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . find the length of train ?

Explanation: "explanation : first person speed = 2 * ( 5 / 18 ) = 5 / 9 m / sec second person speed = 4 * ( 5 / 18 ) = 10 / 9 m / sec let the length of train is x metre and speed is y m / sec then , x / y − 5 / 9 = 9 = > 9 y − 5 = x = > 9 y − x = 5 . . . . . ( i ) also , x / y − 10 / 9 = 10 90 y − 9 x = 100 . . . . . ( ii ) from ( i ) and ( ii ) , we get , x = 50 so length of train is 50 metre option b"

multiply(multiply(subtract(divide(subtract(multiply(2, divide(9, const_3600)), multiply(4, divide(10, const_3600))), subtract(divide(9, const_3600), divide(10, const_3600))), 2), divide(9, const_3600)), const_1000)

<gadget id="calculator">9 / 3_600</gadget>
<output>1/400 = around 0.0025</output>
<gadget id="calculator">2 * (1/400)</gadget>
<output>1/200 = around 0.005</output>
<gadget id="calculator">10 / 3_600</gadget>
<output>1/360 = around 0.002778</output>
<gadget id="calculator">4 * (1/360)</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/200) - (1/90)</gadget>
<output>-11/1_800 = around -0.006111</output>
<gadget id="calculator">(1/400) - (1/360)</gadget>
<output>-1/3_600 = around -0.000278</output>
<gadget id="calculator">(-11/1_800) / (-1/3_600)</gadget>
<output>22</output>
<gadget id="calculator">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">20 * (1/400)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 1_000</gadget>
<output>50</output>
<result>50</result>


a number is doubled and 9 is added . if resultant is trebled , it becomes 63 . what is that number

Explanation: "explanation : = > 3 ( 2 x + 9 ) = 63 = > 2 x + 9 = 21 = > x = 6 answer : option a"

divide(subtract(63, multiply(const_3, 9)), multiply(const_3, const_2))

<gadget id="calculator">3 * 9</gadget>
<output>27</output>
<gadget id="calculator">63 - 27</gadget>
<output>36</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">36 / 6</gadget>
<output>6</output>
<result>6</result>


a 80 cm long wire is to be cut into two pieces so that one piece will be 3 / 5 th of the other , how many centimeters will the shorter piece be ?

Explanation: "explanation : 1 : 3 / 5 = 5 : 3 3 / 8 * 80 = 30 answer : option a"

subtract(80, divide(80, add(divide(3, 5), const_1)))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">80 / (8/5)</gadget>
<output>50</output>
<gadget id="calculator">80 - 50</gadget>
<output>30</output>
<result>30</result>


a waiter ' s salary consists of his salary and tips . during one week his tips were 7 / 4 of his salary . what fraction of his income came from tips ?

Explanation: "income = salary ( s ) + tips = s + s * 7 / 4 = s * 11 / 4 tips = s * 7 / 4 fraction of his income came from tips = ( s * 7 / 4 ) / ( s * 11 / 4 ) = 7 / 11 answer : e"

divide(divide(7, 4), add(divide(7, 4), const_1))

<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">(7/4) + 1</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">(7/4) / (11/4)</gadget>
<output>7/11 = around 0.636364</output>
<result>7/11 = around 0.636364</result>


the total age of a and b is 15 years more than the total age of b and c . c is how many year younger than

Explanation: "given that a + b = 15 + b + c = > a â € “ c = 15 + b â € “ b = 15 = > c is younger than a by 15 years answer : e"

<gadget id="calculator">15 * 1</gadget>
<output>15</output>
<result>15</result>


a bag has 9 green balls and 23 pink balls . how many green balls should be added to the bag so that the ratio of green balls and pink balls in the bag becomes 1 : 1 ?

Explanation: suppose x green balls need to be added . then , the number of green balls becomes 9 + x , and the number of pink balls remains the same , 23 . but now the ratio of green and pink balls is 1 : 1 this means , ( 9 + x ) / 23 = 1 / 1 solving this we get x = 14 . ans e

<gadget id="calculator">23 - 9</gadget>
<output>14</output>
<result>14</result>


what is remainder of the division ( 1625 * 1627 * 1629 ) / 12 ?

Explanation: remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : a

subtract(multiply(multiply(1625, 1627), 1629), subtract(multiply(multiply(1625, 1627), 1629), const_3))


if henry were to add 8 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?

Explanation: "7 / 8 x - 3 / 4 x = 8 galls 1 / 8 * x = 8 gallons x = 64 gallons answer c"

multiply(8, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(7/8) - (3/4)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<result>64</result>


find compound interest on $ 4000 at 15 % per annum for 2 years 4 months , compounded annually .

Explanation: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 4000 x ( 1 +  ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 4000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 5554.50 . : . c . i . = rs . ( 5554.50 - 4000 ) = $ 1554.50 answer a ."

add(add(multiply(4000, divide(15, const_100)), multiply(add(4000, multiply(4000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(4000, multiply(4000, divide(15, const_100))), multiply(add(4000, multiply(4000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">4_000 * (3/20)</gadget>
<output>600</output>
<gadget id="calculator">4_000 + 600</gadget>
<output>4_600</output>
<gadget id="calculator">4_600 * (3/20)</gadget>
<output>690</output>
<gadget id="calculator">600 + 690</gadget>
<output>1_290</output>
<gadget id="calculator">4_600 + 690</gadget>
<output>5_290</output>
<gadget id="calculator">(3/20) / 3</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">5_290 * (1/20)</gadget>
<output>529/2 = around 264.5</output>
<gadget id="calculator">1_290 + (529/2)</gadget>
<output>3_109/2 = around 1_554.5</output>
<result>3_109/2 = around 1_554.5</result>


a train is 485 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 485 + 140 = 625 meter time = distance / speed = 625 ∗ 2 / 25 = 50 seconds option d"

divide(add(485, 140), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">485 + 140</gadget>
<output>625</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">625 / (25/2)</gadget>
<output>50</output>
<result>50</result>


if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1110 will be :

Explanation: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 111 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1110 3.7 z = 1110 , z = 300 answer : . a"

divide(1110, add(add(multiply(add(const_1, divide(25, const_100)), add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))), const_1))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<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">(5/4) * (6/5)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) + (6/5)</gadget>
<output>27/10 = around 2.7</output>
<gadget id="calculator">(27/10) + 1</gadget>
<output>37/10 = around 3.7</output>
<gadget id="calculator">1_110 / (37/10)</gadget>
<output>300</output>
<result>300</result>


a train moves with a speed of 135 kmph . its speed in metres per second is

Explanation: "solution speed = 135 kmph = ( 135 x 5 / 18 ) m / sec = 37.5 m / sec . answer b"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">135 * (5/18)</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>


a 50 ml after - shave lotion at 30 % alcohol is mixed with 30 ml of pure water . what is the percentage of alcohol in the new solution ?

Explanation: the amount of the final mixture is given by 50 ml + 30 ml = 80 ml the amount of alcohol is equal to the amount of alcohol in pure water ( which is 0 ) plus the amount of alcohol in the 30 % solution . let x be the percentage of alcohol in the final solution . hence 0 + 30 % 50 ml = x ( 80 ) solve for x x = 0.1817 = 18.75 % answer c

multiply(divide(divide(multiply(30, 50), const_100), add(50, 30)), const_100)

<gadget id="calculator">30 * 50</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 100</gadget>
<output>15</output>
<gadget id="calculator">50 + 30</gadget>
<output>80</output>
<gadget id="calculator">15 / 80</gadget>
<output>3/16 = around 0.1875</output>
<gadget id="calculator">(3/16) * 100</gadget>
<output>75/4 = around 18.75</output>
<result>75/4 = around 18.75</result>


what is the value of 11 ^ x - 11 ^ ( x + 2 ) , where x is the largest integer such that 11 ^ x is a factor of 30030 ?

Explanation: the given expression is 11 x - 11 ( x ^ + 2 ) = 11 x ( 1 - x ) 1 x needs to be factor of 30030 and x needs to be the largest integer possible . this means 11 x needs to be the largest factor possible . the largest factor of a number is the number itself . the largest factor of 30030 is 30030 = ( 11 * 2730 ) x must be 2730 the value of 11 x ( 1 - x ) = – 1320 . answer : b

<gadget id="calculator">11 ** 3</gadget>
<output>1_331</output>
<gadget id="calculator">11 - 1_331</gadget>
<output>-1_320</output>
<result>-1_320</result>


a ’ s speed is 17 / 14 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?

Explanation: "let x be the fraction of the distance that b runs . let v be the speed at which b runs . the time should be the same for both runners . time = d / ( 17 v / 14 ) = xd / v ( 14 / 17 ) * d / v = x * d / v x = 14 / 17 b should have a head start of 3 / 17 of the full distance . the answer is d ."

<gadget id="calculator">17 - 14</gadget>
<output>3</output>
<gadget id="calculator">3 / 17</gadget>
<output>3/17 = around 0.176471</output>
<result>3/17 = around 0.176471</result>


a invested $ 100 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?

Explanation: "a : b = 100 * 12 : 200 * 6 a : b = 1 : 1 a ' s share = 100 / 2 = $ 50 answer is e"

multiply(100, subtract(const_1, divide(divide(200, const_2), add(100, divide(200, const_2)))))

<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">100 + 100</gadget>
<output>200</output>
<gadget id="calculator">100 / 200</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">100 * (1/2)</gadget>
<output>50</output>
<result>50</result>


in a family 13 people eat only vegetarian , 8 people eat only non veg . , 6 people eat both veg and non veg . . how many people eat veg in the family ?

Explanation: "total people eat veg = only veg + both veg and non veg total = 13 + 6 = 19 answer = c"

<gadget id="calculator">13 + 6</gadget>
<output>19</output>
<result>19</result>


a shopkeeper labeled the price of his articles so as to earn a profit of 40 % on the cost price . he then sold the articles by offering a discount of 5 % on the labeled price . what is the actual percent profit earned in the deal ?

Explanation: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 140 . sp = rs . 140 - 5 % of 140 = rs . 140 - 7 = rs . 133 . gain = rs . 133 â € “ rs . 100 = rs . 33 therefore , gain / profit percent = 33 % . answer : option d"

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

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">140 * (1/20)</gadget>
<output>7</output>
<gadget id="calculator">140 - 7</gadget>
<output>133</output>
<gadget id="calculator">133 - 100</gadget>
<output>33</output>
<result>33</result>


the total of 336 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is

Explanation: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 336 - x ) . 0.20 * ( x ) + 0.25 ( 336 - x ) = 71 = > x = 260 . . answer : d ) 260"

divide(subtract(multiply(336, 25), multiply(71, const_100)), subtract(25, 20))

<gadget id="calculator">336 * 25</gadget>
<output>8_400</output>
<gadget id="calculator">71 * 100</gadget>
<output>7_100</output>
<gadget id="calculator">8_400 - 7_100</gadget>
<output>1_300</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">1_300 / 5</gadget>
<output>260</output>
<result>260</result>


a factory produces 6400 toys per week . if the workers at this factory work 3 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?

Explanation: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 3 days ) by 3 . 6400 / 3 = 2133 toys correct answer b"


walking at 5 / 6 th of its usual speed a cab is 15 mnts late . find its usual time to cover the journey ?

Explanation: new speed = 5 / 6 th of usual speed new time = 6 / 5 th of usual time 6 / 5 ut - ut = 15 m ut / 5 = 15 m ut = 75 m answer is d

<gadget id="calculator">5 * 15</gadget>
<output>75</output>
<result>75</result>


a person purchased a tv set for rs . 16000 and a dvd player for rs . 6250 . he sold both the items together for rs . 35600 . what percentage of profit did he make ?

Explanation: the total cp = rs . 16000 + rs . 6250 = rs . 22250 and sp = rs . 35600 profit ( % ) = ( 35600 - 22250 ) / 22250 * 100 = 60 % answer : d

multiply(subtract(divide(35600, add(16000, 6250)), const_1), const_100)

<gadget id="calculator">16_000 + 6_250</gadget>
<output>22_250</output>
<gadget id="calculator">35_600 / 22_250</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) - 1</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>60</result>


two trains each 180 m in length are running on the same parallel lines in opposite directions with the speed of each 80 kmph . in what time will they cross each other completely ?

Explanation: d = 180 m + 180 m = 360 m * 1 / 1000 = 0.36 kms rs = 80 + 80 = 160 kmph t = ( 0.36 / 160 ) * 3600 = 8.1 sec answer : b

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">80 * (5/18)</gadget>
<output>200/9 = around 22.222222</output>
<gadget id="calculator">180 / (200/9)</gadget>
<output>81/10 = around 8.1</output>
<result>81/10 = around 8.1</result>


20 buckets of water fill a tank when the capacity of each bucket is 13.5 litres . how many buckets will be required to fill the same tank if the capacity of each bucket is 9 litres ?

Explanation: "capacity of the tank = 20 × 13.5 = 270 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 270 ⁄ 9 = 30 answer a"

<gadget id="calculator">13.5 * 20</gadget>
<output>270</output>
<gadget id="calculator">270 / 9</gadget>
<output>30</output>
<result>30</result>


the number of the members of a club is more than 50 and less than 80 . when 4 people sit at a table , other people exactly divided to 8 - people groups ( 8 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 9 - people groups , how many people will be left ?

Explanation: "the number of members is 7 k + 4 = 8 j + 4 the only number in this range which satisfies this is 60 . 60 / 9 = 6 ( 9 ) + 6 the answer is d ."

<gadget id="calculator">lcm(8, 7)</gadget>
<output>56</output>
<gadget id="calculator">56 + 4</gadget>
<output>60</output>
<gadget id="calculator">60 % 9</gadget>
<output>6</output>
<result>6</result>


a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train .

Explanation: "speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : c"

multiply(divide(multiply(72, const_1000), const_3600), 9)

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>
<gadget id="calculator">20 * 9</gadget>
<output>180</output>
<result>180</result>


two clocks are set correctly at 1 0 ' clock in the afternoon . one keeps correct time . the other gains 5 seconds per minute . that evening , when the fast clock shows 6 : 20 , what does the correct clock show ?

Explanation: faster clock gains 5 seconds per minute or 5 * 60 = 300 seconds or 5 minutes per hour . both clocks are set at 1 : 00 at 2 : 00 correct clock is at 2 : 00 faster clock is at 2 : 05 : 00 ( 1 hour + gained 5 minutes ) at 3 : 00 - correct clock is at 3 : 00 faster clock is at 3 : 10 : 00 ( 2 hours + gained 10 minutes ) . in 5 hours , faster clock would gain 20 minutes . it will show 6 : 20 . at that point , the correct clock would show 6 : 00 . answer is c

add(1, divide(add(multiply(5, const_3600), multiply(20, const_60)), add(const_3600, multiply(5, const_60))))

<gadget id="calculator">5 * 3_600</gadget>
<output>18_000</output>
<gadget id="calculator">20 * 60</gadget>
<output>1_200</output>
<gadget id="calculator">18_000 + 1_200</gadget>
<output>19_200</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">3_600 + 300</gadget>
<output>3_900</output>
<gadget id="calculator">19_200 / 3_900</gadget>
<output>64/13 = around 4.923077</output>
<gadget id="calculator">1 + (64/13)</gadget>
<output>77/13 = around 5.923077</output>
<result>77/13 = around 5.923077</result>


Explanation: "1 ^ 3 : 3 ^ 3 = 1 : 27 answer : a"

<gadget id="calculator">1 ** 3</gadget>
<output>1</output>
<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">1 / 27</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>


a shopkeeper sold an article offering a discount of 5 % and earned a profit of 22.55 % . what would have been the percentage of profit earned if no discount was offered ?

Explanation: "let c . p . be rs . 100 . then , s . p . = rs . 122.55 let marked price be rs . x . then , 95 / 100 x = 122.55 x = 12255 / 95 = rs . 129 now , s . p . = rs . 129 , c . p . = rs . 100 profit % = 29 % . answer : b"

subtract(divide(multiply(add(const_100, 22.55), const_100), subtract(const_100, 5)), const_100)

<gadget id="calculator">100 + 22.55</gadget>
<output>122.55</output>
<gadget id="calculator">122.55 * 100</gadget>
<output>12_255</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">12_255 / 95</gadget>
<output>129</output>
<gadget id="calculator">129 - 100</gadget>
<output>29</output>
<result>29</result>


5 men are equal to as many women as are equal to 8 boys . all of them earn $ 90 only . men ’ s wages are ?

Explanation: "b $ 6 5 m = xw = 8 b 5 m + xw + 8 b - - - - - $ 90 rs . 5 m + 5 m + 5 m - - - - - $ 90 rs . 15 m - - - - - - $ 90 = > 1 m = $ 6 ."

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">90 / 15</gadget>
<output>6</output>
<result>6</result>


two trains of equal are running on parallel lines in the same direction at 48 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?

Explanation: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 48 - 36 = 12 km / hr . = 12 * 5 / 18 = 10 / 3 m / sec . 2 x / 36 = 10 / 3 = > x = 60 . answer : a"

divide(multiply(36, divide(multiply(subtract(48, 36), const_1000), const_3600)), const_2)

<gadget id="calculator">48 - 36</gadget>
<output>12</output>
<gadget id="calculator">12 * 1_000</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 3_600</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">36 * (10/3)</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<result>60</result>


a number is said to be prime saturated if the product of all the different positive prime factors of t is less than the square root of t . what is the greatest two digit prime saturated integer ?

Explanation: "t = 96 = 3 * 32 = 3 * 2 ^ 5 answer is d ."

add(multiply(const_2, const_3), subtract(const_100, const_10))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">6 + 90</gadget>
<output>96</output>
<result>96</result>


a cycle is bought for rs . 1500 and sold for rs . 1620 , find the gain percent ?

Explanation: "1500 - - - - 120 100 - - - - ? = > 8 % answer : b"

multiply(divide(subtract(1620, 1500), 1500), const_100)

<gadget id="calculator">1_620 - 1_500</gadget>
<output>120</output>
<gadget id="calculator">120 / 1_500</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 100</gadget>
<output>8</output>
<result>8</result>