a man invested rs . 14,400 in rs . 100 shares of a company at 25 % premium . if the company declares 5 % dividend at the end of the year , then how much does he get ?

Explanation: "solution number of shares = ( 14400 / 125 ) = 115.2 . face value = rs . ( 100 x 115.2 ) = rs . 11520 . annual income = rs . ( 5 / 100 x 11520 ) = rs . 576 . answer a"

multiply(multiply(100, divide(add(add(multiply(const_10, const_1000), multiply(const_4, const_1000)), multiply(const_4, 100)), add(100, multiply(100, divide(25, 100))))), divide(5, 100))

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">10_000 + 4_000</gadget>
<output>14_000</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">14_000 + 400</gadget>
<output>14_400</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">100 * (1/4)</gadget>
<output>25</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">14_400 / 125</gadget>
<output>576/5 = around 115.2</output>
<gadget id="calculator">100 * (576/5)</gadget>
<output>11_520</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">11_520 * (1/20)</gadget>
<output>576</output>
<result>576</result>


a ladder 22 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 7 feet from the base of the wall . if the top of the ladder slips down 3 feet , how many feet will the bottom of the ladder slip ?

Explanation: "22 ^ 2 - 7 ^ 2 = 435 it means that the height is equal to 20.85 . since the top of the ladder slips down 4 feet , then the height of the wall = 20.85 - 3 = 17.85 the bottom = sqrt ( 22 ^ 2 - 17.85 ^ 2 ) = sqrt ( 484 - 318.62 ) = 12.86 ans is a"

sqrt(subtract(power(22, const_2), power(subtract(sqrt(subtract(power(22, const_2), power(7, const_2))), 3), const_2)))

<gadget id="calculator">22 ** 2</gadget>
<output>484</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">484 - 49</gadget>
<output>435</output>
<gadget id="calculator">435 ** (1/2)</gadget>
<output>sqrt(435) = around 20.856654</output>
<gadget id="calculator">(sqrt(435)) - 3</gadget>
<output>-3 + sqrt(435) = around 17.856654</output>
<gadget id="calculator">(-3 + sqrt(435)) ** 2</gadget>
<output>(-3 + sqrt(435))**2 = around 318.860078</output>
<gadget id="calculator">484 - ((-3 + sqrt(435))**2)</gadget>
<output>484 - (-3 + sqrt(435))**2 = around 165.139922</output>
<gadget id="calculator">(484 - (-3 + sqrt(435))**2) ** (1/2)</gadget>
<output>sqrt(484 - (-3 + sqrt(435))**2) = around 12.850678</output>
<result>sqrt(484 - (-3 + sqrt(435))**2) = around 12.850678</result>


water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of hydrogen are there in 117 grams of water ?

Explanation: ( 2 / 18 ) * 117 = 13 grams the answer is d .

<gadget id="calculator">2 + 16</gadget>
<output>18</output>
<gadget id="calculator">117 / 18</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">2 * (13/2)</gadget>
<output>13</output>
<result>13</result>


if a tire rotates at 400 revolutions per minute when the car is traveling 24 km / h , what is the circumference of the tire ?

Explanation: "400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * c = 24,000 m : c is the circumference c = 1 meters correct answer a"

multiply(divide(24, multiply(multiply(multiply(const_2, const_3), const_10), 400)), const_1000)

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 * 400</gadget>
<output>24_000</output>
<gadget id="calculator">24 / 24_000</gadget>
<output>1/1_000 = around 0.001</output>
<gadget id="calculator">(1/1_000) * 1_000</gadget>
<output>1</output>
<result>1</result>


a can do a work in 15 days and b in 20 days . if they work on it together for 7 days , then the fraction of the work that is left is

Explanation: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 7 = 245 remaining work is 300 - 245 = 55 remaining fraction of work is = 55 / 300 = 11 / 60 answer e"

subtract(const_1, multiply(add(divide(const_1, 15), divide(const_1, 20)), 7))

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(7/60) * 7</gadget>
<output>49/60 = around 0.816667</output>
<gadget id="calculator">1 - (49/60)</gadget>
<output>11/60 = around 0.183333</output>
<result>11/60 = around 0.183333</result>


workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.75 lacs . how many workers were they ?

Explanation: n * 50 = ( 375000 - 300000 ) = 75000 n = 75000 / 50 = 1500 d

divide(multiply(multiply(subtract(3.75, 3), const_1000), const_100), 50)

<gadget id="calculator">3.75 - 3</gadget>
<output>0.75</output>
<gadget id="calculator">0.75 * 1_000</gadget>
<output>750</output>
<gadget id="calculator">750 * 100</gadget>
<output>75_000</output>
<gadget id="calculator">75_000 / 50</gadget>
<output>1_500</output>
<result>1_500</result>


40 % of a number is added to 60 , the result is the same number . find the number ?

Explanation: "( 40 / 100 ) * x + 60 = x 4 x + 600 = 10 x 6 x = 600 x = 100 answer : d"

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">60 / (3/5)</gadget>
<output>100</output>
<result>100</result>


what is the smallest integer that is multiple of 5 , 711

Explanation: it is the lcm of 5 , 7 and 11 which is 385 . the answer is c .

multiply(multiply(subtract(const_12, const_1), add(const_3, const_4)), 5)

<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<result>385</result>


the average waight of a , b , c is 45 kg . the avgwgt of a & b be 40 kg & that of b , c be 43 kg . find the wgt of b .

Explanation: sol . let a , b , c represent their individual wgts . then , a + b + c = ( 45 * 3 ) kg = 135 kg a + b = ( 40 * 2 ) kg = 80 kg & b + c = ( 43 * 2 ) kg = 86 kg b = ( a + b ) + ( b + c ) - ( a + b + c ) = ( 80 + 86 - 135 ) kg = 31 kg . answer d

subtract(multiply(40, const_2), subtract(multiply(45, const_3), multiply(43, const_2)))

<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">45 * 3</gadget>
<output>135</output>
<gadget id="calculator">43 * 2</gadget>
<output>86</output>
<gadget id="calculator">135 - 86</gadget>
<output>49</output>
<gadget id="calculator">80 - 49</gadget>
<output>31</output>
<result>31</result>


a father is now 3 times as old as his son . 8 years back , he was 4 times as old as his son . the age of the son ( in years ) is

Explanation: if father ' s age is f and son ' s age is s , then f = 3 s and f - 8 = 4 * ( s - 8 ) 3 s - 5 = 4 s - 32 s = 24 f = 72 years answer : b

<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<gadget id="calculator">32 - 8</gadget>
<output>24</output>
<result>24</result>


in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 40 per square m ?

Explanation: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 40 * 950 = rs . 38000 d"

add(add(multiply(multiply(multiply(20, 15), const_2), 40), multiply(multiply(multiply(20, 5), const_2), 40)), multiply(multiply(multiply(15, 5), const_2), 40))

<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">300 * 2</gadget>
<output>600</output>
<gadget id="calculator">600 * 40</gadget>
<output>24_000</output>
<gadget id="calculator">20 * 5</gadget>
<output>100</output>
<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<gadget id="calculator">200 * 40</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">15 * 5</gadget>
<output>75</output>
<gadget id="calculator">75 * 2</gadget>
<output>150</output>
<gadget id="calculator">150 * 40</gadget>
<output>6_000</output>
<gadget id="calculator">32_000 + 6_000</gadget>
<output>38_000</output>
<result>38_000</result>


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

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

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


a sum of money becomes 7 / 6 of itself in 7 years at a certain rate of simple interest . the rate per annum is ?

Explanation: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 7 years . rate = ( 100 * x ) / ( x * 6 * 7 ) = 50 / 21 % . answer : d"

multiply(divide(subtract(divide(7, 6), const_1), 7), const_100)

<gadget id="calculator">7 / 6</gadget>
<output>7/6 = around 1.166667</output>
<gadget id="calculator">(7/6) - 1</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) / 7</gadget>
<output>1/42 = around 0.02381</output>
<gadget id="calculator">(1/42) * 100</gadget>
<output>50/21 = around 2.380952</output>
<result>50/21 = around 2.380952</result>


a ship 77 km from the shore , springs a leak which admits to 9 / 4 tonnes of water in 11 / 2 minutes . 92 tonnes of water would sink it . but the pumps can throw out 12 tonnes of water per hour . find the average rate of sailing so that the ship may just reach the shore as it begins to sink .

Explanation: leak admits 9 / 4 tonnes water in 11 / 2 min = 11 / 2 * 4 / 9 = 22 / 9 leak admits 9 / 22 tonne of water in 5 min in 1 min in thrws 1 / 5 tonne of water = 9 / 22 - 1 / 5 = 23 / 110 92 / 23 / 11 min = 440 min 22 / 3 min = 7 / 22 / 22 / 3 = > 10.5 km / hr answer a

divide(77, divide(92, subtract(divide(divide(9, 4), divide(divide(11, 2), const_60)), 12)))

<gadget id="calculator">9 / 4</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>
<gadget id="calculator">(11/2) / 60</gadget>
<output>11/120 = around 0.091667</output>
<gadget id="calculator">(9/4) / (11/120)</gadget>
<output>270/11 = around 24.545455</output>
<gadget id="calculator">(270/11) - 12</gadget>
<output>138/11 = around 12.545455</output>
<gadget id="calculator">92 / (138/11)</gadget>
<output>22/3 = around 7.333333</output>
<gadget id="calculator">77 / (22/3)</gadget>
<output>21/2 = around 10.5</output>
<result>21/2 = around 10.5</result>


a library has an average of 600 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :

Explanation: "since the month begins with sunday , to there will be five sundays in the month average required = ( 600 x 5 + 240 x 25 ) / 30 ) = 300 answer : option c"

divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 600), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>
<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 600</gadget>
<output>3_000</output>
<gadget id="calculator">30 - 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>
<gadget id="calculator">3_000 + 6_000</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 / 30</gadget>
<output>300</output>
<result>300</result>


the lcm of two numbers is 2310 and hcf is 30 . if one of the numbers is 210 . then what is the other number ?

Explanation: "first number * second number = lcm * hcf other number = 2310 * 30 / 210 = 11 * 30 = 330 answer : c"

<gadget id="calculator">2_310 * 30</gadget>
<output>69_300</output>
<gadget id="calculator">69_300 / 210</gadget>
<output>330</output>
<result>330</result>


a small college reduced its faculty by approximately 15 percent to 195 professors . what was the original number of faculty members ?

Explanation: "if x is the original number of faculty members , then after 15 % reduction in faculty members number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of faculty members is 229 correct answer - d"

divide(195, divide(subtract(const_100, 15), const_100))

<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">195 / (17/20)</gadget>
<output>3_900/17 = around 229.411765</output>
<result>3_900/17 = around 229.411765</result>


if the sides of a rectangle are increased by 35 % , what is the percentage increase in the area ?

Explanation: if sides are a and b , after increase sides would be 1.35 a and 1.35 b . percentage increase in area = ( 1.35 a * 1.35 b - ab ) * 100 / ab = 82.25 answer : c

multiply(subtract(power(add(divide(35, const_100), const_1), const_2), const_1), const_100)

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) + 1</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(27/20) ** 2</gadget>
<output>729/400 = around 1.8225</output>
<gadget id="calculator">(729/400) - 1</gadget>
<output>329/400 = around 0.8225</output>
<gadget id="calculator">(329/400) * 100</gadget>
<output>329/4 = around 82.25</output>
<result>329/4 = around 82.25</result>


the length of the bridge , which a train 120 m long and traveling at 45 km / hr can cross in 30 sec is ?

Explanation: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 x = 255 m . answer : option e"

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 120)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 120</gadget>
<output>255</output>
<result>255</result>


if a person walks at 20 km / hr instead of 10 km / hr , he would have walked 40 km more . the actual distance traveled by him is ?

Explanation: "let the actual distance traveled be x km . then , x / 10 = ( x + 40 ) / 20 10 x - 400 = > x = 40 km . answer : a"

multiply(10, divide(40, subtract(20, 10)))

<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<result>40</result>


there are 840 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?

Explanation: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 840 . hence , we have m + f = 840 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 840 / 3 = 280 solving the three equations yields the solution f = 280 , m = 560 , and d = 280 . the number of female democratic participants equals half the female participants equals 280 / 2 = 140 . answer : d"

divide(subtract(multiply(divide(840, const_3), const_4), 840), const_2)

<gadget id="calculator">840 / 3</gadget>
<output>280</output>
<gadget id="calculator">280 * 4</gadget>
<output>1_120</output>
<gadget id="calculator">1_120 - 840</gadget>
<output>280</output>
<gadget id="calculator">280 / 2</gadget>
<output>140</output>
<result>140</result>


the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % is ?

Explanation: "let original length = x metres and original breadth = y metres . original area = ( xy ) m 2 . new length = 120 x m = 6 x m . 100 5 new breadth = 120 y m = 6 y m . 100 5 new area = 6 x x 6 y m 2 = 36 xy m 2 . 5 5 25 the difference between the original area = xy and new - area 36 / 25 xy is = ( 36 / 25 ) xy - xy = xy ( 36 / 25 - 1 ) = xy ( 11 / 25 ) or ( 11 / 25 ) xy increase % = 11 xy x 1 x 100 % = 44 % . a )"

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

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * (6/5)</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>


the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 40 degrees . find the temperature on friday ?

Explanation: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 40 tu + w + th = 192 - 40 = 152 f = 184 – 152 = 32 answer : b"

subtract(40, subtract(multiply(48, const_4), multiply(46, const_4)))

<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">46 * 4</gadget>
<output>184</output>
<gadget id="calculator">192 - 184</gadget>
<output>8</output>
<gadget id="calculator">40 - 8</gadget>
<output>32</output>
<result>32</result>


difference between the length & breadth of a rectangle is 30 m . if its perimeter is 300 m , then its area is ? ? we have : ( l - b ) = 30 and 2 ( l + b ) = 300 or ( l + b ) = 150 ?

Explanation: solving the two equations , we get : l = 90 and b = 60 . the ratio of length and breath is 90 : 60 = 3 : 2 e

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


what is the maximum number e of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?

Explanation: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get e = 24 cubes . ans . c

multiply(multiply(divide(12, power(27, inverse(const_3))), divide(9, power(27, inverse(const_3)))), floor(divide(8, power(27, inverse(const_3)))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">8 / 3</gadget>
<output>8/3 = around 2.666667</output>
<gadget id="calculator">floor(8/3)</gadget>
<output>2</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>24</result>


Explanation: since 64 / k = 4 and 64 / 16 = 4 , then k = 16 correct answer a

<gadget id="calculator">64 / 4</gadget>
<output>16</output>
<result>16</result>


Explanation: "1 ^ 3 + 3 ^ 2 = 1 + 9 = 10 3 ^ 3 + 5 ^ 2 = 27 + 25 = 52 5 ^ 3 + 7 ^ 2 = 125 + 49 = 174 and 7 ^ 3 + 11 ^ 2 = 343 + 121 = 464 answer : e"

<gadget id="calculator">7 ** 3</gadget>
<output>343</output>
<gadget id="calculator">11 ** 2</gadget>
<output>121</output>
<gadget id="calculator">343 + 121</gadget>
<output>464</output>
<result>464</result>


10 play kabadi , 30 play kho kho only , 5 play both gmaes . then how many in total ?

Explanation: 10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 30 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 30 + 5 = 35 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 35 - 5 = 40 answer : d

<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<gadget id="calculator">10 + 35</gadget>
<output>45</output>
<gadget id="calculator">45 - 5</gadget>
<output>40</output>
<result>40</result>


14 men make 1400 toy in 5 days 1 day after work 14 more worker join now how may days work can finish

Explanation: 14 men make toy in 5 days after 1 day 14 more worker join m 1 / m 2 = d 2 / d 1 14 / 28 = d 2 / 4 = 2 day answer : b

divide(multiply(multiply(5, 14), subtract(1400, divide(1400, 5))), multiply(multiply(const_2, 14), 1400))

<gadget id="calculator">5 * 14</gadget>
<output>70</output>
<gadget id="calculator">1_400 / 5</gadget>
<output>280</output>
<gadget id="calculator">1_400 - 280</gadget>
<output>1_120</output>
<gadget id="calculator">70 * 1_120</gadget>
<output>78_400</output>
<gadget id="calculator">2 * 14</gadget>
<output>28</output>
<gadget id="calculator">28 * 1_400</gadget>
<output>39_200</output>
<gadget id="calculator">78_400 / 39_200</gadget>
<output>2</output>
<result>2</result>


what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 19.50 ?

Explanation: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 5.50 : 3.50 = 11 : 7"

<gadget id="calculator">25 - 19.5</gadget>
<output>5.5</output>
<gadget id="calculator">19.5 - 16</gadget>
<output>3.5</output>
<gadget id="calculator">5.5 / 3.5</gadget>
<output>1.571429</output>
<result>1.571429</result>


a sum of rs 468.75 was lent out at simple interest and at the end of 1 year and 8 months , the total amount of rs 500 is received . find the rate of interest ?

Explanation: here p = 468.75 which is the principle . amount = rs 500 amount = si + p 500 = [ 468.75 * ( 20 / 12 ) * r ] / 100 + 468.75 31.25 = 156.25 * 5 r / 100 r = 4 % answer : b

divide(divide(multiply(subtract(500, 468.75), const_100), add(1, divide(8, const_12))), 468.75)

<gadget id="calculator">500 - 468.75</gadget>
<output>31.25</output>
<gadget id="calculator">31.25 * 100</gadget>
<output>3_125</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 + (2/3)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">3_125 / (5/3)</gadget>
<output>1_875</output>
<gadget id="calculator">1_875 / 468.75</gadget>
<output>4</output>
<result>4</result>


a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 110 . what was the number he chose ?

Explanation: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 110 x = 124 answer : d"

<gadget id="calculator">110 + 138</gadget>
<output>248</output>
<gadget id="calculator">248 / 2</gadget>
<output>124</output>
<result>124</result>


the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 14 cm each . the radius of the sphere is

Explanation: "solution 4 î r 2 = 2 î 7 x 14 â ‡ ’ r 2 = ( 7 x 14 / 2 ) â ‡ ’ 49 â ‡ ’ r = 7 cm . answer d"

sqrt(divide(multiply(multiply(const_pi, multiply(14, divide(14, const_2))), const_2), multiply(const_pi, const_4)))

<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">14 * 7</gadget>
<output>98</output>
<gadget id="calculator">pi * 98</gadget>
<output>98*pi = around 307.87608</output>
<gadget id="calculator">(98*pi) * 2</gadget>
<output>196*pi = around 615.75216</output>
<gadget id="calculator">pi * 4</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(196*pi) / (4*pi)</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<result>7</result>


if 8 men or 12 women can do a piece of work in 30 days , in how many days can the same work be done by 6 men and 11 women ?

Explanation: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 30 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 30 = 1 / 360 so , 20 women work = 20 / 360 = 1 / 18 ans : 18 days answer : e"

inverse(add(divide(6, multiply(8, 30)), divide(11, multiply(12, 30))))

<gadget id="calculator">8 * 30</gadget>
<output>240</output>
<gadget id="calculator">6 / 240</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">12 * 30</gadget>
<output>360</output>
<gadget id="calculator">11 / 360</gadget>
<output>11/360 = around 0.030556</output>
<gadget id="calculator">(1/40) + (11/360)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">1 / (1/18)</gadget>
<output>18</output>
<result>18</result>


set s consists of integers { 8 , 11 , 12 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 25 % . what is the value of integer n ?

Explanation: the average of the numbers in set s is 12 . if we increase the mean by 25 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d .

<gadget id="calculator">12 + 14</gadget>
<output>26</output>
<gadget id="calculator">26 + 14</gadget>
<output>40</output>
<result>40</result>


the average marks obtained by 50 candidates in a certain examination is 40 . find the total marks .

Explanation: following the above formula , we have the total marks = 50 * 40 = 2000 answer is b

<gadget id="calculator">50 * 40</gadget>
<output>2_000</output>
<result>2_000</result>


the speed of a car is 95 km in the first hour and 60 km in the second hour . what is the average speed of the car ?

Explanation: "s = ( 95 + 60 ) / 2 = 77.5 kmph answer : c"

<gadget id="calculator">95 + 60</gadget>
<output>155</output>
<gadget id="calculator">155 / 2</gadget>
<output>155/2 = around 77.5</output>
<result>155/2 = around 77.5</result>


a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 30 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?

Explanation: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 30 = 2.5 km . the time it takes the hiker to complete this distance is 2.5 / 4 hours = 37.5 minutes the cyclist needs to wait 37.5 - 5 = 32.5 minutes the answer is e ."

multiply(divide(subtract(multiply(30, divide(5, const_60)), multiply(4, divide(5, const_60))), 4), const_60)

<gadget id="calculator">5 / 60</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">30 * (1/12)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">4 * (1/12)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(5/2) - (1/3)</gadget>
<output>13/6 = around 2.166667</output>
<gadget id="calculator">(13/6) / 4</gadget>
<output>13/24 = around 0.541667</output>
<gadget id="calculator">(13/24) * 60</gadget>
<output>65/2 = around 32.5</output>
<result>65/2 = around 32.5</result>


3 ltr of water is added with 9 ltr of a solution containing 57 % of alcohol in the water . the % of alcohol in the new mixture is ?

Explanation: "we have a 9 litre solution containing 57 % of alcohol in the water . = > quantity of alcohol in the solution = 9 ã — 57 / 100 now 3 litre of water is added to the solution . = > total quantity of the new solution = 9 + 3 = 12 percentage of alcohol in the new solution = 9 ã — 57 / 100 12 ã — 100 = 9 ã — 5710012 ã — 100 = 9 ã — 4.75 / 100 = 42.75 % b"

multiply(const_100, divide(multiply(divide(57, const_100), 9), add(3, 9)))

<gadget id="calculator">57 / 100</gadget>
<output>57/100 = around 0.57</output>
<gadget id="calculator">(57/100) * 9</gadget>
<output>513/100 = around 5.13</output>
<gadget id="calculator">3 + 9</gadget>
<output>12</output>
<gadget id="calculator">(513/100) / 12</gadget>
<output>171/400 = around 0.4275</output>
<gadget id="calculator">100 * (171/400)</gadget>
<output>171/4 = around 42.75</output>
<result>171/4 = around 42.75</result>


a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 11.00 ?

Explanation: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 11 ( 1 / 12 ) * x = 11 x = 132 answer : d"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">0.5 / 3</gadget>
<output>0.166667</output>
<gadget id="calculator">(1/4) - 0.166667</gadget>
<output>0.083333</output>
<gadget id="calculator">11 / 0.083333</gadget>
<output>132.000528</output>
<result>132.000528</result>


the length and breadth of a rectangle is increased by 5 % and 15 % respectively . what is the increase in the area ?

Explanation: "100 * 100 = 10000 105 * 115 = 12075 - - - - - - - - - - - 2075 10000 - - - - - - 2075 100 - - - - - ? = > 20.75 answer d"

divide(multiply(subtract(rectangle_area(add(5, const_100), add(15, const_100)), rectangle_area(const_100, const_100)), const_100), rectangle_area(const_100, const_100))

<gadget id="calculator">5 + 100</gadget>
<output>105</output>
<gadget id="calculator">15 + 100</gadget>
<output>115</output>
<gadget id="calculator">105 * 115</gadget>
<output>12_075</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">12_075 - 10_000</gadget>
<output>2_075</output>
<gadget id="calculator">2_075 * 100</gadget>
<output>207_500</output>
<gadget id="calculator">207_500 / 10_000</gadget>
<output>83/4 = around 20.75</output>
<result>83/4 = around 20.75</result>


a train running at the speed of 40 km / hr crosses a pole in 9 seconds . what is the length of the train ?

Explanation: "speed = 40 x 5 / 18 m / sec = 100 / 9 m / sec . length of the train = ( speed x time ) . length of the train = 100 / 9 x 9 m = 100 m . answer : e"

multiply(divide(multiply(40, const_1000), const_3600), 9)

<gadget id="calculator">40 * 1_000</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 3_600</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) * 9</gadget>
<output>100</output>
<result>100</result>


a chemical supply company has 60 liters of a 35 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?

Explanation: "60 liters of a 35 % hno 3 solution means hno 3 = 21 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 21 + x = 50 % of ( 60 + x ) or x = 18 hence , a"

multiply(subtract(divide(60, const_2), divide(multiply(60, 35), const_100)), const_2)

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">60 * 35</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 / 100</gadget>
<output>21</output>
<gadget id="calculator">30 - 21</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<result>18</result>


the batting average of a particular batsman is 60 runs in 46 innings . if the difference in his highest and lowest score is 140 runs and his average excluding these two innings is 58 runs , find his highest score .

Explanation: "explanation : total runs scored by the batsman = 60 * 46 = 2760 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2760 â € “ 2552 = 208 runs . let the highest score be x , hence the lowest score = x â € “ 140 x + ( x - 140 ) = 208 2 x = 348 x = 174 runs answer : e"

divide(add(140, subtract(multiply(60, 46), multiply(58, subtract(46, const_2)))), const_2)

<gadget id="calculator">60 * 46</gadget>
<output>2_760</output>
<gadget id="calculator">46 - 2</gadget>
<output>44</output>
<gadget id="calculator">58 * 44</gadget>
<output>2_552</output>
<gadget id="calculator">2_760 - 2_552</gadget>
<output>208</output>
<gadget id="calculator">140 + 208</gadget>
<output>348</output>
<gadget id="calculator">348 / 2</gadget>
<output>174</output>
<result>174</result>


Explanation: here from equation 1 we will get m ^ 2 - 8 m + 1 = 0 m ^ 2 = 8 m - 1 m = ( 8 m - 1 ) / m . . . . . . . . . ( 1 ) m = 8 - 1 / m so m + 1 / m = 8 now in equation 2 m ^ 3 + 1 / m ^ 3 ( m + 1 / m ) ( m ^ 2 - m * 1 / m + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 - 1 + 1 / m ^ 2 ) ( m + 1 / m ) ( m ^ 2 + 1 / m ^ 2 - 1 ) ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 m * 1 / m - 1 } { since a ^ 2 + b ^ 2 = ( a + b ) ^ 2 - 2 ab } ( m + 1 / m ) { ( m + 1 / m ) ^ 2 - 2 - 1 } now putting the value of m from equation 1 8 ( 8 ^ 2 - 2 - 1 ) 8 ( 64 - 3 ) = 488 answer : b

power(divide(add(add(const_4, const_4), sqrt(add(add(const_10, const_10), multiply(const_10, const_4)))), 2), 3)

<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">20 + 40</gadget>
<output>60</output>
<gadget id="calculator">60 ** (1/2)</gadget>
<output>2*sqrt(15) = around 7.745967</output>
<gadget id="calculator">8 + (2*sqrt(15))</gadget>
<output>2*sqrt(15) + 8 = around 15.745967</output>
<gadget id="calculator">(2*sqrt(15) + 8) / 2</gadget>
<output>sqrt(15) + 4 = around 7.872983</output>
<gadget id="calculator">(sqrt(15) + 4) ** 3</gadget>
<output>(sqrt(15) + 4)**3 = around 487.997951</output>
<result>(sqrt(15) + 4)**3 = around 487.997951</result>


if 3 a – 3 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?

Explanation: when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c

subtract(subtract(add(subtract(subtract(subtract(subtract(subtract(subtract(subtract(32, 4), 4), const_2), const_2), const_1), 3), const_1), 2), 3), const_4)

<gadget id="calculator">32 - 4</gadget>
<output>28</output>
<gadget id="calculator">28 - 4</gadget>
<output>24</output>
<gadget id="calculator">24 - 2</gadget>
<output>22</output>
<gadget id="calculator">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">19 - 3</gadget>
<output>16</output>
<gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">17 - 3</gadget>
<output>14</output>
<gadget id="calculator">14 - 4</gadget>
<output>10</output>
<result>10</result>


in a group of 100 cars , 47 cars do not have air conditioning . if at least 55 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?

Explanation: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 55 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 55 . . we have to assign atleast 8 tocars with ac and racing stripes . hence ac = 53 - 8 = 45 . the answer is a"

<gadget id="calculator">100 - 55</gadget>
<output>45</output>
<result>45</result>


at a certain conference , 78 % of the attendees registered at least two weeks in advance and paid their conference fee in full . if 10 % of the attendees who paid their conference fee in full did not register at least two weeks in advance , what percent of conference attendees registered at least two weeks in advance ?

Explanation: i do not think that venn will be helpful here . a table will make more sense . but here is my approach . 78 % regestered at least 2 weeks and paid full fee . 10 % paid full fee and did not registered at least 2 weeks in advance . then 90 % paid full fee and registered at least 2 weeks before . 90 % * x = 78 % where x is the number of people who registerd 2 weeks in advance and paid full fee . ( answer d )

divide(multiply(78, const_100), subtract(const_100, 10))

<gadget id="calculator">78 * 100</gadget>
<output>7_800</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">7_800 / 90</gadget>
<output>260/3 = around 86.666667</output>
<result>260/3 = around 86.666667</result>


if the volume of two cubes are in the ratio 8 : 1 , the ratio of their edges is :

Explanation: explanation : let the edges be a and b of two cubes , then a 3 / b 3 = 8 / 1 = > ( a / b ) 3 = ( 2 / 1 ) 3 a / b = 2 / 1 = > a : b = 2 : 1 option a

<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>
<result>2</result>


what is the dividend . divisor 15 , the quotient is 8 and the remainder is 5

Explanation: "d = d * q + r d = 15 * 8 + 5 d = 120 + 5 d = 125 answer : d"

<gadget id="calculator">15 * 8</gadget>
<output>120</output>
<gadget id="calculator">120 + 5</gadget>
<output>125</output>
<result>125</result>


x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 20 days . how long will y take to complete the work ?

Explanation: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 20 days whole work will be done by y in 20 * 5 / 4 = 25 days answer is c"

multiply(20, inverse(subtract(const_1, divide(8, 40))))

<gadget id="calculator">8 / 40</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / (4/5)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">20 * (5/4)</gadget>
<output>25</output>
<result>25</result>


by selling an article at rs . 500 , a profit of 25 % is made . find its cost price ?

Explanation: "sp = 500 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 500 * [ 100 / ( 100 + 25 ) ] = 500 * [ 100 / 125 ] = rs . 400 answer : a"

divide(multiply(500, const_100), add(const_100, 25))

<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">50_000 / 125</gadget>
<output>400</output>
<result>400</result>


in a class of 32 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?

Explanation: "total = english + german - both + neither - - > 40 = english + 22 - 12 + 0 - - > english = 22 - - > only english = english - both = 22 - 12 = 10 . answer : b ."

<gadget id="calculator">32 + 12</gadget>
<output>44</output>
<gadget id="calculator">44 - 22</gadget>
<output>22</output>
<gadget id="calculator">22 - 12</gadget>
<output>10</output>
<result>10</result>


the ratio of radius of a circle and the side of a square is 2 : 5 . find the ratio of their areas :

Explanation: "radius / side = 2 / 5 â ‡ ’ area of circle / area of square = 4 / 25 answer : b"

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) ** 2</gadget>
<output>4/25 = around 0.16</output>
<result>4/25 = around 0.16</result>


a lion chases a pony 7 hours after the pony runs . lion takes 8 hours to reach the pony . if the average speed of the lion is 49 kmph , what s the average speed of the pony ?

Explanation: pony take 15 hours and lion take 8 hours . . . then distance chased by them is 49 * 8 . so speed of pony is ( 49 * 8 ) / 15 = 29.4 kmph . answer is e

divide(multiply(49, 8), multiply(7, const_2))

<gadget id="calculator">49 * 8</gadget>
<output>392</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">392 / 14</gadget>
<output>28</output>
<result>28</result>


on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 360 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?

Explanation: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 360 ) = 2 + 2 ( extra ) = > 2 x - 720 = x = > x = 720 . answer : e"

<gadget id="calculator">360 * 2</gadget>
<output>720</output>
<result>720</result>


the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is ?

Explanation: "cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">106.25 - (1/4)</gadget>
<output>106</output>
<result>106</result>


a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 900 , what is the reduced price for kg ?

Explanation: "a 900 * ( 25 / 100 ) = 225 - - - - 5 ? - - - - 1 = > rs . 45"

divide(divide(multiply(900, 25), const_100), 5)

<gadget id="calculator">900 * 25</gadget>
<output>22_500</output>
<gadget id="calculator">22_500 / 100</gadget>
<output>225</output>
<gadget id="calculator">225 / 5</gadget>
<output>45</output>
<result>45</result>


rectangular tile each of size 80 cm by 55 cm must be laid horizontally on a rectangular floor of size 210 cm by 330 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :

Explanation: "area of tile = 80 * 55 = 4400 area of floor = 210 * 330 = 72600 no of tiles = 72600 / 4400 = 16.5 so , the no of tile = 16 answer : b"

divide(multiply(210, 330), multiply(80, 55))

<gadget id="calculator">210 * 330</gadget>
<output>69_300</output>
<gadget id="calculator">80 * 55</gadget>
<output>4_400</output>
<gadget id="calculator">69_300 / 4_400</gadget>
<output>63/4 = around 15.75</output>
<result>63/4 = around 15.75</result>


sowdharya had 90 currency notes in all , some of which are of rs 95 denomination and the remaining of rs 45 denomination . the total amount of all these currency notes was rs . 5000 . how much amount ( in rs ) did she have in the denomination of rs 45 ?

Explanation: let the number of 45 - rupee notes = x then , the number of 95 - rupee notes = ( 90 – x ) 45 x + 95 ( 90 – x ) = 5000 : x = 71 answer : c

subtract(90, divide(subtract(5000, multiply(90, 45)), subtract(95, 45)))

<gadget id="calculator">90 * 45</gadget>
<output>4_050</output>
<gadget id="calculator">5_000 - 4_050</gadget>
<output>950</output>
<gadget id="calculator">95 - 45</gadget>
<output>50</output>
<gadget id="calculator">950 / 50</gadget>
<output>19</output>
<gadget id="calculator">90 - 19</gadget>
<output>71</output>
<result>71</result>


if an investor puts $ 700 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?

Explanation: "1.05 * 1.05 * 700 = $ 771.75 the answer is b ."

multiply(700, power(add(const_1, divide(divide(10, const_2), const_100)), const_2))

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">700 * (441/400)</gadget>
<output>3_087/4 = around 771.75</output>
<result>3_087/4 = around 771.75</result>


a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?

Explanation: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 12000 answer : b"

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">600 / (1/20)</gadget>
<output>12_000</output>
<result>12_000</result>


to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . find how many parts the company made and how many days this took .

Explanation: let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 ⋅ 25 + ( x − 3 ) ⋅ 30 = 75 + 30 ( x − 3 ) therefore : 25 x = 75 + 30 ( x − 3 ) − 100 25 x = 75 + 30 x − 90 − 100 190 − 75 = 30 x − 25 115 = 5 x x = 23 so the company worked 23 days and they made 23 ⋅ 25 + 100 = 675 pieces . so answer is e .

add(multiply(divide(subtract(add(multiply(add(25, 5), 3), 100), multiply(25, 3)), 5), 25), 100)

<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 3</gadget>
<output>90</output>
<gadget id="calculator">90 + 100</gadget>
<output>190</output>
<gadget id="calculator">25 * 3</gadget>
<output>75</output>
<gadget id="calculator">190 - 75</gadget>
<output>115</output>
<gadget id="calculator">115 / 5</gadget>
<output>23</output>
<gadget id="calculator">23 * 25</gadget>
<output>575</output>
<gadget id="calculator">575 + 100</gadget>
<output>675</output>
<result>675</result>


a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weights 8 g / cm cube , then find the weight of the pipe .

Explanation: explanation : in this type of question , we need to subtract external radius and internal radius to get the answer using the volume formula as the pipe is hollow . oh ! line become a bit complicated , sorry for that , lets solve it . external radius = 4 cm internal radius = 3 cm [ because thickness of pipe is 1 cm ] volume of iron = π r 2 h = 22 / 7 ∗ [ 42 − 32 ] ∗ 21 cm 3 = 22 / 7 ∗ 1 ∗ 21 cm 3 = 462 cm 3 weight of iron = 462 * 8 = 3696 gm = 3.696 kg option a

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), const_1), 21)), 8), const_1000)

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


village x has a population of 72000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?

Explanation: "let the population of two villages be equal after p years then , 72000 - 1200 p = 42000 + 800 p 2000 p = 30000 p = 15 answer is a ."

<gadget id="calculator">72_000 - 42_000</gadget>
<output>30_000</output>
<gadget id="calculator">800 + 1_200</gadget>
<output>2_000</output>
<gadget id="calculator">30_000 / 2_000</gadget>
<output>15</output>
<result>15</result>


a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is :

Explanation: let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : option c

divide(40, subtract(add(multiply(40, add(const_1, divide(10, const_100))), multiply(50, add(const_1, divide(20, const_100)))), multiply(90, add(const_1, divide(15, const_100)))))

<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">40 * (11/10)</gadget>
<output>44</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">50 * (6/5)</gadget>
<output>60</output>
<gadget id="calculator">44 + 60</gadget>
<output>104</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">90 * (23/20)</gadget>
<output>207/2 = around 103.5</output>
<gadget id="calculator">104 - (207/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">40 / (1/2)</gadget>
<output>80</output>
<result>80</result>


find the remainder of the division ( 3 ^ 33 ) / 7 .

Explanation: find the pattern of the remainders after each power : ( 3 ^ 1 ) / 7 remainder 3 ( 3 ^ 2 ) / 7 remainder 2 ( 3 ^ 3 ) / 7 remainder 6 ( 3 ^ 4 ) / 7 remainder 4 ( 3 ^ 5 ) / 7 remainder 5 ( 3 ^ 6 ) / 7 remainder 1 - - > this is where the cycle ends ( 3 ^ 7 ) / 7 remainder 3 - - > this is where the cycle begins again ( 3 ^ 8 ) / 7 remainder 2 continuing the pattern to ( 3 ^ 33 ) / 7 gives us a remainder of 6 final answer : e ) 6

<gadget id="calculator">3 ** 33</gadget>
<output>5_559_060_566_555_523</output>
<gadget id="calculator">5_559_060_566_555_523 % 7</gadget>
<output>6</output>
<result>6</result>


an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 4 ?

Explanation: "let the number of meters to be examined be x then , 0.05 % of x = 4 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 4 x = 8000 answer is b"

<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">400 / 0.05</gadget>
<output>8_000</output>
<result>8_000</result>


a train passes a platform in 34 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is

Explanation: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 34 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 34 = > 300 + l = 15 × 34 = 510 = > l = 510 - 300 = 210 meter answer : option c"

multiply(multiply(const_0_2778, 54), subtract(34, 20))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">34 - 20</gadget>
<output>14</output>
<gadget id="calculator">15 * 14</gadget>
<output>210</output>
<result>210</result>


the average age of 15 students of a class is 15 years . out of these , the average age of 3 students is 14 years and that of the other 11 students is 16 years . the age of the 15 th student is

Explanation: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 3 + 16 x 11 ) ] = ( 225 - 218 ) = 7 years . answer d"

subtract(multiply(15, 15), add(multiply(3, 14), multiply(11, 16)))

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">3 * 14</gadget>
<output>42</output>
<gadget id="calculator">11 * 16</gadget>
<output>176</output>
<gadget id="calculator">42 + 176</gadget>
<output>218</output>
<gadget id="calculator">225 - 218</gadget>
<output>7</output>
<result>7</result>


a number x is 6 times another number y . the percentage that y is less than x is

Explanation: say y = 1 and x = 6 . then y = 1 is less than x = 6 by ( 6 - 1 ) / 6 * 100 = 5 / 6 * 100 = 83.3 % . answer : b .

multiply(divide(subtract(6, const_1), 6), const_100)

<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/6) * 100</gadget>
<output>250/3 = around 83.333333</output>
<result>250/3 = around 83.333333</result>


liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 10 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )

Explanation: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 30 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 30 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 30 mph therefore answer is d"

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">10 + 20</gadget>
<output>30</output>
<result>30</result>


what is the compound interest paid on a sum of rs . 3000 for the period of 2 years at 10 % per annum .

Explanation: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3000 = 3000 * ( 21 / 100 ) = 630 answer a"

subtract(multiply(3000, power(add(const_1, divide(10, const_100)), 2)), 3000)

<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">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">3_000 * (121/100)</gadget>
<output>3_630</output>
<gadget id="calculator">3_630 - 3_000</gadget>
<output>630</output>
<result>630</result>


a boy perform 5 times a reaction and his reading are 2 , 2.1 , 2 , 2.2 but unfortunately 5 th reading clearly not visible because a drop of chemical fall onto it . but luckily he have mean of all reading which is 2 . please help him in finding 5 th reading .

Explanation: solution let 5 th reading be x ( 2 + 2.1 + 2 + 2.2 + x ) / 5 = 2 8.3 + x = 10 x = 1.7 answer b

subtract(subtract(subtract(subtract(multiply(2, 5), 2), 2.1), 2), 2.2)

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 - 2</gadget>
<output>8</output>
<gadget id="calculator">8 - 2.1</gadget>
<output>5.9</output>
<gadget id="calculator">5.9 - 2</gadget>
<output>3.9</output>
<gadget id="calculator">3.9 - 2.2</gadget>
<output>1.7</output>
<result>1.7</result>


thirty percent of the members of a swim club have passed the lifesaving test . among the members who have not passed the test , 12 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?

Explanation: 30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 12 = 42 members have not passed the test , thus 0.7 * total = 42 - - > total = 60 . answer : a .

divide(add(12, 30), divide(subtract(const_100, 30), const_100))

<gadget id="calculator">12 + 30</gadget>
<output>42</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">42 / (7/10)</gadget>
<output>60</output>
<result>60</result>


a certain rectangular window is ( 1 / 3 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?

Explanation: 2 x + 2 y = 28 x + y = 14 x + ( 1 / 3 ) x = 14 4 x = 14 * 3 x = 10.5 answer c

<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>11</result>


there are 8 teams in a certain league and each team plays each of the other teams exactly once . if each game is played by 2 teams , what is the total number of games played ?

Explanation: "number of ways 2 teams can be selected out of 8 teams : c 8 / 2 = 8 ∗ 7 / 2 = 28 ans : ' ' c ' '"

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

<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


3 candidates in an election and received 1136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?

Explanation: "total number of votes polled = ( 1136 + 7636 + 11628 ) = 20400 so , required percentage = 11628 / 20400 * 100 = 57 % c"

<gadget id="calculator">1_136 + 7_636</gadget>
<output>8_772</output>
<gadget id="calculator">8_772 + 11_628</gadget>
<output>20_400</output>
<gadget id="calculator">11_628 / 20_400</gadget>
<output>57/100 = around 0.57</output>
<gadget id="calculator">(57/100) * 100</gadget>
<output>57</output>
<result>57</result>


at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 3 years ?

Explanation: "explanation : 250 = ( 1750 x 3 xr ) / 100 r = 4.76 % answer : option c"

multiply(divide(divide(subtract(2000, 1750), 1750), 3), const_100)

<gadget id="calculator">2_000 - 1_750</gadget>
<output>250</output>
<gadget id="calculator">250 / 1_750</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) / 3</gadget>
<output>1/21 = around 0.047619</output>
<gadget id="calculator">(1/21) * 100</gadget>
<output>100/21 = around 4.761905</output>
<result>100/21 = around 4.761905</result>


the perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )

Explanation: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 19 + 14 ) = 66 cm perimeter of the square = 66 cm i . e . 4 a = 66 a = 16.5 diameter of the semicircle = 16.5 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16.5 ) = 1 / 2 ( 22 / 7 ) ( 16.5 ) = 25.93 cm to two decimal places answer : e"

floor(divide(circumface(divide(divide(multiply(const_2, add(14, 19)), const_4), const_2)), const_2))

<gadget id="calculator">14 + 19</gadget>
<output>33</output>
<gadget id="calculator">2 * 33</gadget>
<output>66</output>
<gadget id="calculator">66 / 4</gadget>
<output>33/2 = around 16.5</output>
<gadget id="calculator">(33/2) / 2</gadget>
<output>33/4 = around 8.25</output>
<gadget id="calculator">2 * pi * (33/4)</gadget>
<output>33*pi/2 = around 51.836279</output>
<gadget id="calculator">(33*pi/2) / 2</gadget>
<output>33*pi/4 = around 25.918139</output>
<gadget id="calculator">floor(33*pi/4)</gadget>
<output>25</output>
<result>25</result>


john and steve are speed walkers in a race . john is 15 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

Explanation: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 15 + 2 - - - > 0.5 t = 17 - - - > t = 34 seconds . d is the correct answer ."

<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">3.7 * 17</gadget>
<output>62.9</output>
<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>
<gadget id="calculator">62.9 / 0.5</gadget>
<output>125.8</output>
<gadget id="calculator">125.8 + 17</gadget>
<output>142.8</output>
<gadget id="calculator">142.8 / 4.2</gadget>
<output>34</output>
<result>34</result>


a ratio between two numbers is 3 : 4 and their l . c . m . is 84 . the first number is

Explanation: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 84 ⇔ x = 7 . hence , the first number is 21 . answer c"

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">84 / 12</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<result>21</result>


the principal that amounts to rs . 4813 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?

Explanation: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4813 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4036 . answer : b"

divide(4813, power(add(1, divide(add(6, divide(1, 4)), const_100)), 3))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">6 + (1/4)</gadget>
<output>25/4 = around 6.25</output>
<gadget id="calculator">(25/4) / 100</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 + (1/16)</gadget>
<output>17/16 = around 1.0625</output>
<gadget id="calculator">(17/16) ** 3</gadget>
<output>4_913/4_096 = around 1.199463</output>
<gadget id="calculator">4_813 / (4_913/4_096)</gadget>
<output>19_714_048/4_913 = around 4_012.629351</output>
<result>19_714_048/4_913 = around 4_012.629351</result>


the area of a rectangular plot is 18 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?

Explanation: "l × b = 18 × b ∴ l = 18 m and l – b = 10 ∴ b = 18 – 10 = 8 m answer b"

<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<result>8</result>


in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 38500 . how many times did he participate in the competition ?

Explanation: 38500 = 2 * 2 * 5 * 5 * 5 * 7 * 11 john participated 7 times . the answer is b .

floor(sqrt(divide(38500, multiply(multiply(multiply(11, 7), 5), 2))))

<gadget id="calculator">11 * 7</gadget>
<output>77</output>
<gadget id="calculator">77 * 5</gadget>
<output>385</output>
<gadget id="calculator">385 * 2</gadget>
<output>770</output>
<gadget id="calculator">38_500 / 770</gadget>
<output>50</output>
<gadget id="calculator">50 ** (1/2)</gadget>
<output>5*sqrt(2) = around 7.071068</output>
<gadget id="calculator">floor(5*sqrt(2))</gadget>
<output>7</output>
<result>7</result>


the first flight out of phoenix airport had a late departure . if the next 3 flights departed on - time , how many subsequent flights need to depart from phoenix on - time , for the airport ' s on - time departure rate to be higher than 40 % ?

Explanation: we need on - time departure rate to be higher than 4 / 10 , so it should be at least 5 / 11 , which means that 5 out of 11 flights must depart on time . since for now 3 out of 4 flights departed on time then 5 - 3 = 2 subsequent flights need to depart on - time . answer : d

add(floor(multiply(divide(40, const_100), 3)), const_1)

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 3</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">floor(6/5)</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<result>2</result>


two years ago , ram put $ 500 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 600 . the next year , his account balance increased by 10 % . at the end of the two years , by what percent has ram ' s account balance increased from his initial deposit of $ 500 ?

Explanation: investment 500 dollars 1 st year total gained = 100 total amount end of first year = 600 second year account increased by 10 % = 600 * 0.1 = 60 therefore total amount by second year end = 660 so total percentage increase in money = ( 660 - 500 ) * 100 / 500 = 32 % correct answer d = 32 %

multiply(divide(add(multiply(divide(10, const_100), 600), 100), 500), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 600</gadget>
<output>60</output>
<gadget id="calculator">60 + 100</gadget>
<output>160</output>
<gadget id="calculator">160 / 500</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>


if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 3 and 100 respectively , then the sum of the reciprocal of the numbers is equal to :

Explanation: let the numbers be a and b . then , a + b = 45 and ab = 3 * 100 = 300 . required sum = 1 / a + 1 / b = ( a + b ) / ab = 103 / 300 answer : a

<gadget id="calculator">3 + 100</gadget>
<output>103</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">103 / 300</gadget>
<output>103/300 = around 0.343333</output>
<result>103/300 = around 0.343333</result>


mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 45 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?

Explanation: "let me try a simpler one . lets assume that candidate got 45 % votes and total votes is 100 . candidate won = 45 remaining = 55 to get 50 % , candidate requires 5 votes from 100 which is 5 % and 5 votes from 55 . 5 / 55 = 1 / 11 = . 09 = 9 % which is approx 9 % . hence the answer is a ."

multiply(divide(subtract(divide(50, const_100), divide(45, const_100)), subtract(const_1, divide(45, const_100))), const_100)

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(1/2) - (9/20)</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (9/20)</gadget>
<output>11/20 = around 0.55</output>
<gadget id="calculator">(1/20) / (11/20)</gadget>
<output>1/11 = around 0.090909</output>
<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>100/11 = around 9.090909</result>


pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

Explanation: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 12 = > 1 / x = 1 / 6 - 1 / 12 = ( 2 - 1 ) / 12 = 1 / 12 = > x = 12 . answer : e"

divide(multiply(12, 6), subtract(12, 6))

<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<gadget id="calculator">12 - 6</gadget>
<output>6</output>
<gadget id="calculator">72 / 6</gadget>
<output>12</output>
<result>12</result>


w and x start a business with rs . 5000 and rs . 20000 respectively . hoe should they share their profits at the end of one year ?

Explanation: they should share the profits in the ratio of their investments . the ratio of the investments made by w and x = 5000 : 20000 = > 1 : 4 . answer : c

divide(multiply(5000, const_12), multiply(20000, const_12))

<gadget id="calculator">5_000 * 12</gadget>
<output>60_000</output>
<gadget id="calculator">20_000 * 12</gadget>
<output>240_000</output>
<gadget id="calculator">60_000 / 240_000</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 130 marks , the no of questions he attempts correctly is :

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 80 – x ) = 130 = > 5 x = 210 = > x = 42 answer : e"

<gadget id="calculator">130 + 80</gadget>
<output>210</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">210 / 5</gadget>
<output>42</output>
<result>42</result>


what is the least number should be added to 1056 , so the sum of the number is completely divisible by 29 ?

Explanation: ( 1056 / 29 ) gives remainder 12 17 + 12 = 29 , so we need to add 17 a

subtract(multiply(add(floor(divide(1056, 29)), const_1), 29), 1056)

<gadget id="calculator">1_056 / 29</gadget>
<output>1_056/29 = around 36.413793</output>
<gadget id="calculator">floor(1_056/29)</gadget>
<output>36</output>
<gadget id="calculator">36 + 1</gadget>
<output>37</output>
<gadget id="calculator">37 * 29</gadget>
<output>1_073</output>
<gadget id="calculator">1_073 - 1_056</gadget>
<output>17</output>
<result>17</result>


an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1455 , what was the total number of pairs of contact lenses that she sold ?

Explanation: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a

<gadget id="calculator">150 * 5</gadget>
<output>750</output>
<gadget id="calculator">1_455 - 750</gadget>
<output>705</output>
<gadget id="calculator">150 + 85</gadget>
<output>235</output>
<gadget id="calculator">705 / 235</gadget>
<output>3</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 3</gadget>
<output>11</output>
<result>11</result>


if the price of an article went up by 30 % , then by what percent should it be brought down to bring it back to its original price ?

Explanation: "let the price of the article be rs . 100 . 30 % of 100 = 30 . new price = 100 + 30 = rs . 130 required percentage = ( 130 - 100 ) / 130 * 100 = 30 / 130 * 100 = 23 1 / 13 % answer : b"

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

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">30 / 130</gadget>
<output>3/13 = around 0.230769</output>
<gadget id="calculator">(3/13) * 100</gadget>
<output>300/13 = around 23.076923</output>
<result>300/13 = around 23.076923</result>


if n is the product of all the integers from 5 to 20 , inclusive , what is the greatest integer k for which 2 ^ k is a factor of n ?

Explanation: 20 / 2 = 10 10 / 2 = 5 ans : 10 + 5 = 15 answer : e

add(add(add(add(add(add(add(const_1, const_3), const_1), 2), const_1), const_4), const_1), 2)

<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<gadget id="calculator">13 + 2</gadget>
<output>15</output>
<result>15</result>


the perimeter of an isosceles right triangle is 14 + 14 sq rt 2 . what is the length of the hypotenuse of the triangle ?

Explanation: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 14 + 14 sqrt 2 or , a . ( 2 + sqrt 2 ) = 14 ( 1 + sqrt 2 ) , a = 14 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 14 * 2.414 / 3.414 = then hypotenuse = 9.899 e"

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">14 * (sqrt(2))</gadget>
<output>14*sqrt(2) = around 19.79899</output>
<gadget id="calculator">(14*sqrt(2)) / 2</gadget>
<output>7*sqrt(2) = around 9.899495</output>
<result>7*sqrt(2) = around 9.899495</result>


country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 9 % . if ron imported a $ 18000 imported car and ended up paying $ 1950 in taxes , what is the first tier ' s price level ?

Explanation: let t be the tier price , p be total price = 18000 per the given conditions : 0.12 t + 0.09 ( p - t ) = 1950 0.12 t + 0.09 * 18000 - 0.09 t = 1950 0.03 t + 1620 = 1950 0.03 t = 1950 - 1620 = 330 t = 330 / 0.03 = 11000 answer b

divide(subtract(1950, multiply(divide(9, const_100), 18000)), subtract(divide(12, const_100), divide(9, const_100)))

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">(9/100) * 18_000</gadget>
<output>1_620</output>
<gadget id="calculator">1_950 - 1_620</gadget>
<output>330</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) - (9/100)</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">330 / (3/100)</gadget>
<output>11_000</output>
<result>11_000</result>


a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 7 th of the other , how many centimeters will the shorter piece be ?

Explanation: "explanation : 1 : 2 / 7 = 7 : 2 2 / 9 * 90 = 20 answer : option b"

subtract(90, divide(90, add(divide(2, 7), const_1)))

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(2/7) + 1</gadget>
<output>9/7 = around 1.285714</output>
<gadget id="calculator">90 / (9/7)</gadget>
<output>70</output>
<gadget id="calculator">90 - 70</gadget>
<output>20</output>
<result>20</result>


the sum of 3 integers is 33 . the largest integer is 3 times the middle integer , and the smallest integer is 23 less than the largest integer . what is the product of the 3 integers ?

Explanation: let x be the middle integer . then the largest is 3 x and the smallest is 3 x - 23 . 3 x - 23 + x + 3 x = 33 x = 8 the three integers are 1 , 8 , and 24 . the product is 1 * 8 * 24 = 192 the answer is a .

multiply(multiply(divide(multiply(add(33, 23), 3), add(const_3, const_4)), divide(divide(multiply(add(33, 23), 3), add(const_3, const_4)), 3)), subtract(divide(multiply(add(33, 23), 3), add(const_3, const_4)), 23))

<gadget id="calculator">33 + 23</gadget>
<output>56</output>
<gadget id="calculator">56 * 3</gadget>
<output>168</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">168 / 7</gadget>
<output>24</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<gadget id="calculator">24 * 8</gadget>
<output>192</output>
<gadget id="calculator">24 - 23</gadget>
<output>1</output>
<gadget id="calculator">192 * 1</gadget>
<output>192</output>
<result>192</result>


joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 70 . he was allowed to drop his lowest score . after doing so , his average test score improved to 75 . what is the lowest test score that was dropped ?

Explanation: "the arithmetic mean of 4 equally weighted tests was 70 . so what we can assume is that we have 4 test scores , each 70 . he dropped his lowest score and the avg went to 75 . this means that the lowest score was not 70 and other three scores had given the lowest score 5 each to make it up to 70 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 70 . so the lowest score = 70 - 15 = 55 answer ( c )"

subtract(multiply(70, 4), multiply(75, const_3))

<gadget id="calculator">70 * 4</gadget>
<output>280</output>
<gadget id="calculator">75 * 3</gadget>
<output>225</output>
<gadget id="calculator">280 - 225</gadget>
<output>55</output>
<result>55</result>


an error 2 % in excess is made while measuring the sideofa square . the % of error in the calculated area of the square is ?

Explanation: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 102 x 102 ) cm 2 . ( a 2 - a 1 ) = [ ( 102 ) 2 - ( 100 ) 2 ] = ( 102 + 100 ) x ( 102 - 100 ) = 404 cm 2 . percentage error = 404 x 100 % = 4.04 % 100 x 100 b"

divide(multiply(subtract(square_area(add(const_100, 2)), square_area(const_100)), const_100), square_area(const_100))

<gadget id="calculator">100 + 2</gadget>
<output>102</output>
<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_404 - 10_000</gadget>
<output>404</output>
<gadget id="calculator">404 * 100</gadget>
<output>40_400</output>
<gadget id="calculator">40_400 / 10_000</gadget>
<output>101/25 = around 4.04</output>
<result>101/25 = around 4.04</result>


what is the normal price of an article sold at $ 144 after two successive discounts of 10 % and 20 % ?

Explanation: "0.8 * 0.9 * cost price = $ 144 cost price = $ 200 the answer is c ."

divide(144, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), 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 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">144 / (18/25)</gadget>
<output>200</output>
<result>200</result>


the length of a room is 6.5 m and width is 2.75 m . what is the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .

Explanation: "area = 6.5 * 2.75 sq . metre . cost for sq . metre . = rs . 600 hence , total cost = 6.5 * 2.75 * 600 = rs . 10725 answer : d"

<gadget id="calculator">6.5 * 2.75</gadget>
<output>17.875</output>
<gadget id="calculator">600 * 17.875</gadget>
<output>10_725</output>
<result>10_725</result>


the number of diagonals of a polygon of n sides is given by the formula v = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?

Explanation: "v = n ( n - 3 ) v = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"

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


if 15 % of 30 % of 50 % of a number is 108 , then what is the number ?

Explanation: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 108 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 108 = > a = 10 * 20 * 10 * 2 = 4800 . answer : d"

divide(108, multiply(multiply(divide(50, const_100), divide(30, const_100)), divide(15, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/2) * (3/10)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * (3/20)</gadget>
<output>9/400 = around 0.0225</output>
<gadget id="calculator">108 / (9/400)</gadget>
<output>4_800</output>
<result>4_800</result>


andy solves problems 75 to 125 inclusive in a math exercise . how many problems does he solve ?

Explanation: "125 - 75 + 1 = 51 ' c ' is the answer"

<gadget id="calculator">125 - 75</gadget>
<output>50</output>
<gadget id="calculator">50 + 1</gadget>
<output>51</output>
<result>51</result>


6 ) a marketing firm determined that , of 260 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?

Explanation: "180 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 180 = > 4 x = 120 = > x = 30 answer - c"

divide(subtract(subtract(260, 80), 60), const_4)

<gadget id="calculator">260 - 80</gadget>
<output>180</output>
<gadget id="calculator">180 - 60</gadget>
<output>120</output>
<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<result>30</result>


26 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 = 26 ã — 13.5 = 351 litres when the capacity of each bucket = 9 litres , then the required no . of buckets = 351 â  „ 9 = 39 answer b"

<gadget id="calculator">13.5 * 26</gadget>
<output>351</output>
<gadget id="calculator">351 / 9</gadget>
<output>39</output>
<result>39</result>


a train is running at a speed of 40 km / hr and it crosses a post in 22.5 seconds . what is the length of the train ?

Explanation: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 22.5 s distance covered , d = vt = ( 400 / 36 ) ã — 22.5 = 250 m distance covered is equal to the length of the train = 250 m correct answer is 250 metres e"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">40 * (5/18)</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">22.5 * (100/9)</gadget>
<output>250</output>
<result>250</result>


a 70 kg metal bar made of alloy of tin and silver lost 7 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?

Explanation: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 7 kg when 70 kg alloy is immersed . this is a loss of ( 7 / 70 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"

divide(divide(subtract(7, multiply(divide(0.375, 5), 70)), subtract(divide(1.375, 10), divide(0.375, 5))), subtract(70, divide(subtract(7, multiply(divide(0.375, 5), 70)), subtract(divide(1.375, 10), divide(0.375, 5)))))

<gadget id="calculator">0.375 / 5</gadget>
<output>0.075</output>
<gadget id="calculator">0.075 * 70</gadget>
<output>5.25</output>
<gadget id="calculator">7 - 5.25</gadget>
<output>1.75</output>
<gadget id="calculator">1.375 / 10</gadget>
<output>0.1375</output>
<gadget id="calculator">0.1375 - 0.075</gadget>
<output>0.0625</output>
<gadget id="calculator">1.75 / 0.0625</gadget>
<output>28</output>
<gadget id="calculator">70 - 28</gadget>
<output>42</output>
<gadget id="calculator">28 / 42</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


what is the rate percent when the simple interest on rs . 720 amount to rs . 180 in 4 years ?

Explanation: "180 = ( 720 * 4 * r ) / 100 r = 6.25 % answer : a"

divide(multiply(const_100, 180), multiply(720, 4))

<gadget id="calculator">100 * 180</gadget>
<output>18_000</output>
<gadget id="calculator">720 * 4</gadget>
<output>2_880</output>
<gadget id="calculator">18_000 / 2_880</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>


when 242 is divided by a certain divisor the remainder obtained is 15 . when 698 is divided by the same divisor the remainder obtained is 27 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 5 . what is the value of the divisor ?

Explanation: let that divisor be x since remainder is 15 or 27 it means divisor is greater than 27 . now 242 - 15 = 227 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 27 = 671 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 227 + 671 ) + 15 + 27 = x ( k + l ) + 42 when we divide this number by x then remainder will be equal to remainder of ( 42 divided by x ) = 5 hence x = 42 - 5 = 37 hence e

<gadget id="calculator">15 + 27</gadget>
<output>42</output>
<gadget id="calculator">42 - 5</gadget>
<output>37</output>
<result>37</result>


gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 15 times as heavy as water ?

Explanation: "let us say , water weighs 1 kg / 1 liter . then gold weighs 19 kgs and copper weighs 9 kgs . assume x kgs of gold and y kgs of copper required to get the required alloy . we use weighted average formula = ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 ax = n 1 . a 1 + n 2 . a 2 n 1 + n 2 therefore , 15 = x . 19 + y . 9 x + y 15 = x . 19 + y . 9 x + y 15 x + 15 y = 19 x + 9 y 4 x = 6 y ⇒ x / y = 3 : 2 so gold and copper should be mixed in the ratio 3 : 2 . answer : a"

divide(subtract(15, 9), subtract(19, 15))

<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<gadget id="calculator">19 - 15</gadget>
<output>4</output>
<gadget id="calculator">6 / 4</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


find the cost of fencing around a circular field of diameter 32 m at the rate of rs . 2 a meter ?

Explanation: "2 * 22 / 7 * 16 = 100.5 100.5 * 2 = rs . 201 answer : a"

<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<gadget id="calculator">2 * pi * 16</gadget>
<output>32*pi = around 100.530965</output>
<gadget id="calculator">(32*pi) * 2</gadget>
<output>64*pi = around 201.06193</output>
<result>64*pi = around 201.06193</result>


a bookseller has two display windows . she plans to display 3 new fiction books in the left window , and 3 new non - fiction books in the right window . assuming she can put the 4 fiction books in any order , and separately , the 3 non - fiction books in any order , how many total configurations will there be for the two display windows ?

Explanation: the left window will have permutations of the 3 fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 the right window will have permutations of the 3 non - fiction books , so the number of possibilities for that window is permutations = 3 ! = ( 3 ) ( 2 ) ( 1 ) = 6 any of the 24 displays of the left window could be combined with any of the 6 displays of the right window , so the total number of configurations is 6 * 6 = 36 answer : d .

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<result>36</result>


if julie rows 32 km upstream and 72 km down steam taking 4 hours each , then the speed of the stream

Explanation: speed upstream = 32 / 4 = 8 kmph speed down stream = 72 / 8 = 9 kmph speed of stream = ½ ( 9 - 8 ) = 0.5 kmph answer : b

subtract(divide(divide(subtract(divide(72, 4), divide(32, 4)), const_2), const_2), const_2)

<gadget id="calculator">72 / 4</gadget>
<output>18</output>
<gadget id="calculator">32 / 4</gadget>
<output>8</output>
<gadget id="calculator">18 - 8</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 2</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) - 2</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 7 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?

Explanation: "let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 7 x = 6 / 7 x so if gold card balance is transferred then the rest unspent will be 6 / 7 x - x / 6 = 29 / 42 x so the ans is b"

subtract(1, add(multiply(inverse(3), inverse(const_2)), inverse(7)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/3) * (1/2)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/6) + (1/7)</gadget>
<output>13/42 = around 0.309524</output>
<gadget id="calculator">1 - (13/42)</gadget>
<output>29/42 = around 0.690476</output>
<result>29/42 = around 0.690476</result>


of all the homes on gotham street , 1 / 3 are termite - ridden , and 4 / 7 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?

Explanation: "the fraction of homes which are termite - infested but not collapsing is 3 / 7 * 1 / 3 = 1 / 7 the answer is e ."

divide(add(1, const_2.0), multiply(3, 7))

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 7</gadget>
<output>21</output>
<gadget id="calculator">3 / 21</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>


what is the minimum value of | x - 4 | + | x + 5 | + | x - 5 | ?

Explanation: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 5 | > = 0 - - > minimum occurs at x = - 5 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 5 - - > result = 9 + 0 + 10 = 19 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 9 + 1 = 10 x = 5 - - > result = 1 + 10 + 0 = 11 so minimum value of the expression occurs at x = 4 and the resultant value = 10 answer : e"

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


sravan travelled for 15 hours . he covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph . find the distance travelled by sravan ?

Explanation: let the distance travelled be x km . total time = ( x / 2 ) / 45 + ( x / 2 ) / 30 = 15 = > x / 90 + x / 60 = 15 = > ( 2 x + 3 x ) / 180 = 15 = > x = 540 km answer : b

divide(multiply(45, multiply(30, 30)), add(45, 30))

<gadget id="calculator">30 * 30</gadget>
<output>900</output>
<gadget id="calculator">45 * 900</gadget>
<output>40_500</output>
<gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">40_500 / 75</gadget>
<output>540</output>
<result>540</result>


50 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?

Explanation: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 50 = 66.67 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 66.67 = 100 litres . answer c"

multiply(1200, multiply(800, divide(50, multiply(800, 600))))

<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>
<gadget id="calculator">50 / 480_000</gadget>
<output>1/9_600 = around 0.000104</output>
<gadget id="calculator">800 * (1/9_600)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1_200 * (1/12)</gadget>
<output>100</output>
<result>100</result>


a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 4 - inch increase in the length of the shoe . if the largest size of this shoe is 10 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?

Explanation: "let x be the length of the size 8 shoe . then 0.1 x = 9 / 4 x = 90 / 4 inches the size 15 shoe has a length of 90 / 4 + 7 / 4 = 97 / 4 = 24.25 inches the answer is d ."

add(divide(multiply(divide(1, 4), subtract(17, 8)), divide(10, const_100)), multiply(subtract(15, 8), divide(1, 4)))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">17 - 8</gadget>
<output>9</output>
<gadget id="calculator">(1/4) * 9</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(9/4) / (1/10)</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">15 - 8</gadget>
<output>7</output>
<gadget id="calculator">7 * (1/4)</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">(45/2) + (7/4)</gadget>
<output>97/4 = around 24.25</output>
<result>97/4 = around 24.25</result>


excluding stoppages , the average speed of a bus is 75 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

Explanation: "in 1 hr , the bus covers 75 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 75 - 40 ) km i . e 35 km at 75 km / hr . stoppage time = 35 / 75 hrs = 28 min answer : e"

subtract(multiply(const_1, const_60), multiply(divide(40, 75), const_60))

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">40 / 75</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">(8/15) * 60</gadget>
<output>32</output>
<gadget id="calculator">60 - 32</gadget>
<output>28</output>
<result>28</result>


find the area of a parallelogram with base 26 cm and height 16 cm ?

Explanation: "area of a parallelogram = base * height = 26 * 16 = 416 cm 2 answer : d"

<gadget id="calculator">26 * 16</gadget>
<output>416</output>
<result>416</result>


by selling an article at rs . 600 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?

Explanation: "sp = 600 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / 125 ] = 480 loss = 25 % = 25 % of 480 = rs . 120 sp = cp - loss = 480 - 120 = rs . 360 answer : a"

subtract(divide(multiply(600, const_100), add(25, const_100)), divide(multiply(divide(multiply(600, const_100), add(25, const_100)), 25), const_100))

<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">60_000 / 125</gadget>
<output>480</output>
<gadget id="calculator">480 * 25</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<gadget id="calculator">480 - 120</gadget>
<output>360</output>
<result>360</result>


the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 600 per sq . metre .

Explanation: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 600 × 20.625 ) = 12375 . answer a"

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">600 * 20.625</gadget>
<output>12_375</output>
<result>12_375</result>