ramesh has solved 108 questions in an examination . if he got only ‘ 0 ’ marks , then how many questions were wrong when one mark is given for each one correct answer and 1 / 3 mark is subtracted on each wrong answer .

Explanation: if ramesh attempts ' x ' questions correct and ' y ' questions wrong , then x + y = 108 - - - ( i ) & x - ( 1 / 3 ) y = 0 - - - ( ii ) on solving x = 27 , y = 81 answer : d

subtract(108, divide(multiply(divide(1, 3), 108), add(const_1, divide(1, 3))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 108</gadget>
<output>36</output>
<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">36 / (4/3)</gadget>
<output>27</output>
<gadget id="calculator">108 - 27</gadget>
<output>81</output>
<result>81</result>


what is the measure of the angle x made by the diagonals of the any adjacent sides of a cube .

Explanation: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be x = 60 . c"

<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<result>60</result>


after decreasing 15 % in the price of an article costs rs . 915 . find the actual cost of an article ?

Explanation: "cp * ( 85 / 100 ) = 915 cp = 10.76 * 100 = > cp = 1076 answer : c"

divide(915, subtract(const_1, divide(15, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 - (3/20)</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">915 / (17/20)</gadget>
<output>18_300/17 = around 1_076.470588</output>
<result>18_300/17 = around 1_076.470588</result>


dan can do a job alone in 15 hours . annie , working alone , can do the same job in just 10 hours . if dan works alone for 12 hours and then stops , how many hours will it take annie , working alone , to complete the job ?

Explanation: "dan can complete 1 / 15 of the job per hour . in 12 hours , dan completes 12 ( 1 / 15 ) = 4 / 5 of the job . annie can complete 1 / 10 of the job per hour . to complete the job , annie will take 1 / 5 / 1 / 10 = 2 hours . the answer is a ."

multiply(subtract(const_1, divide(12, 15)), 10)

<gadget id="calculator">12 / 15</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 10</gadget>
<output>2</output>
<result>2</result>


a circle graph shows how the megatech corporation allocates its research and development budget : 17 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?

Explanation: here all percentage when summed we need to get 100 % . as per data 17 + 24 + 15 + 29 + 8 = 93 % . so remaining 7 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 7 % will be 26 degrees . . imo option c .

divide(multiply(subtract(const_100, add(add(add(add(17, 24), 15), 29), 8)), divide(const_3600, const_10)), const_100)

<gadget id="calculator">17 + 24</gadget>
<output>41</output>
<gadget id="calculator">41 + 15</gadget>
<output>56</output>
<gadget id="calculator">56 + 29</gadget>
<output>85</output>
<gadget id="calculator">85 + 8</gadget>
<output>93</output>
<gadget id="calculator">100 - 93</gadget>
<output>7</output>
<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">7 * 360</gadget>
<output>2_520</output>
<gadget id="calculator">2_520 / 100</gadget>
<output>126/5 = around 25.2</output>
<result>126/5 = around 25.2</result>


peter invests a sum of money and gets back an amount of $ 830 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?

Explanation: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 830 = 24 interest earned for 3 years = 24 * 3 = 72 amount invested = 830 - 72 = 758 answer : d"

subtract(830, multiply(divide(subtract(854, 830), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100)))

<gadget id="calculator">854 - 830</gadget>
<output>24</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(1/25) - (3/100)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">24 / (1/100)</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 * (3/100)</gadget>
<output>72</output>
<gadget id="calculator">830 - 72</gadget>
<output>758</output>
<result>758</result>


the simple interest in 14 months on a certain sum at the rate of 6 per cent per annum is 250 more than the interest on the same sum at the rate of 8 per cent in 8 months . how much amount was borrowed ?

Explanation: let the amount be x . from the question , x × 14 × 6 / 1200 − x × 8 × 8 / 1200 = 250 ∴ x = 15000 answer a

divide(250, subtract(multiply(divide(14, const_12), divide(6, const_100)), multiply(divide(8, const_12), divide(8, const_100))))

<gadget id="calculator">14 / 12</gadget>
<output>7/6 = around 1.166667</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(7/6) * (3/50)</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/3) * (2/25)</gadget>
<output>4/75 = around 0.053333</output>
<gadget id="calculator">(7/100) - (4/75)</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">250 / (1/60)</gadget>
<output>15_000</output>
<result>15_000</result>


if $ 120 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?

Explanation: "120 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 120 + 120 * ( r / 100 ) * ( 3 ) = 240 = > r = 100 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 450 answer is e ."

add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(240, 120), 120), 120), 3)), 120))

<gadget id="calculator">150 * 6</gadget>
<output>900</output>
<gadget id="calculator">240 - 120</gadget>
<output>120</output>
<gadget id="calculator">120 * 120</gadget>
<output>14_400</output>
<gadget id="calculator">14_400 / 120</gadget>
<output>120</output>
<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<gadget id="calculator">900 * 40</gadget>
<output>36_000</output>
<gadget id="calculator">36_000 / 120</gadget>
<output>300</output>
<gadget id="calculator">150 + 300</gadget>
<output>450</output>
<result>450</result>


a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 9 : 6 : 5 , respectively , by weight . if 40 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?

Explanation: we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 9 x + 6 x + 5 x = 40 20 x = 40 x = 2 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 5 ) ( 2 ) = 10 pounds of apples = ( 9 ) ( 2 ) = 18 thus we know that there are 18 – 10 = 8 more pounds of apples than grapes . answer is c .

subtract(multiply(9, const_2), multiply(5, const_2))

<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">18 - 10</gadget>
<output>8</output>
<result>8</result>


the population of a town increases 20 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1500 . then what is the population of the town 2 years ago ?

Explanation: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1500 * 100 / 120 * 100 / 125 = 1000 answer : option a"

divide(1500, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(6/5) * (5/4)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">1_500 / (3/2)</gadget>
<output>1_000</output>
<result>1_000</result>


find the average of all the numbers between 6 and 34 which are divisible by 5 .

Explanation: "solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 5 = 20 . answer b"

divide(add(add(6, const_4), subtract(34, const_4)), const_2)

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">34 - 4</gadget>
<output>30</output>
<gadget id="calculator">10 + 30</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.24 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]

Explanation: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 24 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 8 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 16 eggs = 16 / 12 * 24 = 32 cents . answer : c ."

multiply(divide(divide(8, divide(const_1, const_2)), const_12), multiply(0.24, 100))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">8 / (1/2)</gadget>
<output>16</output>
<gadget id="calculator">16 / 12</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">0.24 * 100</gadget>
<output>24</output>
<gadget id="calculator">(4/3) * 24</gadget>
<output>32</output>
<result>32</result>


a train running at the speed of 162 km / hr crosses a pole in 9 seconds . find the length of the train .

Explanation: "speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d"

multiply(divide(multiply(162, const_1000), const_3600), 9)

<gadget id="calculator">162 * 1_000</gadget>
<output>162_000</output>
<gadget id="calculator">162_000 / 3_600</gadget>
<output>45</output>
<gadget id="calculator">45 * 9</gadget>
<output>405</output>
<result>405</result>


a student has to obtain 30 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?

Explanation: "let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b"

divide(add(150, 30), divide(30, const_100))

<gadget id="calculator">150 + 30</gadget>
<output>180</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">180 / (3/10)</gadget>
<output>600</output>
<result>600</result>


a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 5 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?

Explanation: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c"

divide(multiply(5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1))

<gadget id="calculator">8 * 60</gadget>
<output>480</output>
<gadget id="calculator">5 * 480</gadget>
<output>2_400</output>
<gadget id="calculator">6 * 60</gadget>
<output>360</output>
<gadget id="calculator">480 / 360</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">2_400 / (1/3)</gadget>
<output>7_200</output>
<result>7_200</result>


we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 560 . how many green hats did we buy ?

Explanation: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ."

<gadget id="calculator">85 * 6</gadget>
<output>510</output>
<gadget id="calculator">560 - 510</gadget>
<output>50</output>
<result>50</result>


the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1498 respectively . what is the rate of interest ?

Explanation: "1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ."

divide(multiply(subtract(1498, 1400), const_100), 1400)

<gadget id="calculator">1_498 - 1_400</gadget>
<output>98</output>
<gadget id="calculator">98 * 100</gadget>
<output>9_800</output>
<gadget id="calculator">9_800 / 1_400</gadget>
<output>7</output>
<result>7</result>


a man can row 9 kmph in still water . when the river is running at 3.1 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e"

multiply(divide(multiply(add(9, 3.1), subtract(9, 3.1)), add(add(9, 3.1), subtract(9, 3.1))), const_2)

<gadget id="calculator">9 + 3.1</gadget>
<output>12.1</output>
<gadget id="calculator">9 - 3.1</gadget>
<output>5.9</output>
<gadget id="calculator">12.1 * 5.9</gadget>
<output>71.39</output>
<gadget id="calculator">12.1 + 5.9</gadget>
<output>18</output>
<gadget id="calculator">71.39 / 18</gadget>
<output>3.966111</output>
<gadget id="calculator">3.966111 * 2</gadget>
<output>7.932222</output>
<result>7.932222</result>


a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio :

Explanation: "n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer : option d"

divide(multiply(105, const_2), multiply(88, const_3))

<gadget id="calculator">105 * 2</gadget>
<output>210</output>
<gadget id="calculator">88 * 3</gadget>
<output>264</output>
<gadget id="calculator">210 / 264</gadget>
<output>35/44 = around 0.795455</output>
<result>35/44 = around 0.795455</result>


a man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?

Explanation: "let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 15 b - 15 c = 5 b + 5 c , - - > b = 2 c , - - > d = 15 b - 15 b / 2 = 15 b / 2 . interval = \ frac { d } { b } = \ frac { 15 / 2 b } { b } = 15 / 2 answer : e ( 15 / 2 minutes ) ."

divide(subtract(15, divide(15, divide(add(5, 15), subtract(15, 5)))), const_1)

<gadget id="calculator">5 + 15</gadget>
<output>20</output>
<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">15 - (15/2)</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) / 1</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>


rakesh ' s mathematics test had 75 problems , 10 arithmetic , 30 algebra , 35 geometry problems . although he answered 70 % of arithmetic , 40 % of arithmetic and 60 % of geometry problems correctly , still he got less than 60 % problems right . how many more questions he would have to answer more to get passed ?

Explanation: explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a

subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100)))

<gadget id="calculator">75 * 60</gadget>
<output>4_500</output>
<gadget id="calculator">4_500 / 100</gadget>
<output>45</output>
<gadget id="calculator">10 * 70</gadget>
<output>700</output>
<gadget id="calculator">700 / 100</gadget>
<output>7</output>
<gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>
<gadget id="calculator">7 + 12</gadget>
<output>19</output>
<gadget id="calculator">35 * 60</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 / 100</gadget>
<output>21</output>
<gadget id="calculator">19 + 21</gadget>
<output>40</output>
<gadget id="calculator">45 - 40</gadget>
<output>5</output>
<result>5</result>


a number x is multiplied by 7 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?

Explanation: "sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b"

<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<result>7/3 = around 2.333333</result>


one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?

Explanation: connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d

divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))

<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) / 6</gadget>
<output>5/36 = around 0.138889</output>
<gadget id="calculator">1 - (5/36)</gadget>
<output>31/36 = around 0.861111</output>
<gadget id="calculator">1 / (31/36)</gadget>
<output>36/31 = around 1.16129</output>
<result>36/31 = around 1.16129</result>


in the manufacture of a certain product , 6 percent of the units produced are defective and 5 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?

Explanation: "0.06 * 0.05 = 0.003 = 0.3 % the answer is b ."

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">6 * (1/20)</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>


in a group of ducks and cows , the total number of legs are 26 more than twice the no . of heads . find the total no . of buffaloes .

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c"

<gadget id="calculator">26 / 2</gadget>
<output>13</output>
<result>13</result>


a man walking at 3 / 4 th of the speed , reaches his office late by 2 hours . what is the usual time ?

Explanation: at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c

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

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * (3/4)</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(9/8) * 2</gadget>
<output>9/4 = around 2.25</output>
<gadget id="calculator">(3/2) - (9/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(9/4) / (3/8)</gadget>
<output>6</output>
<result>6</result>


given a + b = 1 , find the value of 2 a + 2 b . two solutions are presented below . only one is correct , even though both yield the correct answer .

Explanation: because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<result>2</result>


a sum fetched total simple interest of 4016.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?

Explanation: "let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a"

divide(multiply(const_100, 4016.25), multiply(9, 5))

<gadget id="calculator">100 * 4_016.25</gadget>
<output>401_625</output>
<gadget id="calculator">9 * 5</gadget>
<output>45</output>
<gadget id="calculator">401_625 / 45</gadget>
<output>8_925</output>
<result>8_925</result>


a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 7 , ab = 5 and ac = 11 , what is the length of ae ?

Explanation: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 7 = 21 the answer is b ."

add(add(11, divide(subtract(11, 5), 2)), 7)

<gadget id="calculator">11 - 5</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">11 + 3</gadget>
<output>14</output>
<gadget id="calculator">14 + 7</gadget>
<output>21</output>
<result>21</result>


each of the integers from 1 to 17 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?

Explanation: "out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )"

<gadget id="calculator">17 / 2</gadget>
<output>17/2 = around 8.5</output>
<gadget id="calculator">(17/2) + 1</gadget>
<output>19/2 = around 9.5</output>
<result>19/2 = around 9.5</result>


the averge score of a cricketer for 10 matches is 45 runs . if the average for the first 6 matches is 48 . then find the average for the last 4 matches ?

Explanation: sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d

divide(subtract(multiply(45, 10), multiply(6, 48)), 4)

<gadget id="calculator">45 * 10</gadget>
<output>450</output>
<gadget id="calculator">6 * 48</gadget>
<output>288</output>
<gadget id="calculator">450 - 288</gadget>
<output>162</output>
<gadget id="calculator">162 / 4</gadget>
<output>81/2 = around 40.5</output>
<result>81/2 = around 40.5</result>


a shopkeeper fixes the marked price of an item 40 % above its cost price . the percentage of discount allowed to gain 8 % is

Explanation: "explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b"

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

<gadget id="calculator">8 + 100</gadget>
<output>108</output>
<gadget id="calculator">40 + 100</gadget>
<output>140</output>
<gadget id="calculator">108 / 140</gadget>
<output>27/35 = around 0.771429</output>
<gadget id="calculator">(27/35) * 100</gadget>
<output>540/7 = around 77.142857</output>
<gadget id="calculator">100 - (540/7)</gadget>
<output>160/7 = around 22.857143</output>
<result>160/7 = around 22.857143</result>


how long does a train 60 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?

Explanation: "b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b"

divide(add(60, 80), multiply(60, const_0_2778))

<gadget id="calculator">60 + 80</gadget>
<output>140</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">140 / (50/3)</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>


a circle graph shows how the budget of a certain company was spent : 55 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?

Explanation: "the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ."

divide(multiply(const_360, subtract(const_100, add(add(add(add(55, 9), 5), 4), 2))), const_100)

<gadget id="calculator">55 + 9</gadget>
<output>64</output>
<gadget id="calculator">64 + 5</gadget>
<output>69</output>
<gadget id="calculator">69 + 4</gadget>
<output>73</output>
<gadget id="calculator">73 + 2</gadget>
<output>75</output>
<gadget id="calculator">100 - 75</gadget>
<output>25</output>
<gadget id="calculator">360 * 25</gadget>
<output>9_000</output>
<gadget id="calculator">9_000 / 100</gadget>
<output>90</output>
<result>90</result>


which is the least number that must be subtracted from 1856 so that the remainder when divided by 7 , 12 , 10 is 4 ?

Explanation: first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b

<gadget id="calculator">lcm(7, 12)</gadget>
<output>84</output>
<gadget id="calculator">lcm(84, 10)</gadget>
<output>420</output>
<gadget id="calculator">gcd(1_856, 420)</gadget>
<output>4</output>
<gadget id="calculator">4 * 420</gadget>
<output>1_680</output>
<gadget id="calculator">4 + 1_680</gadget>
<output>1_684</output>
<gadget id="calculator">1_856 - 1_684</gadget>
<output>172</output>
<result>172</result>


how many bricks , each measuring 25 cm * 11.25 cm * 6 cm , will be needed to build a wall 8 m * 6 m * 22.5 m

Explanation: "to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a"

divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

<gadget id="calculator">8 * 100</gadget>
<output>800</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>
<gadget id="calculator">480_000 * 22.5</gadget>
<output>10_800_000</output>
<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>
<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>
<gadget id="calculator">10_800_000 / 1_687.5</gadget>
<output>6_400</output>
<result>6_400</result>


a soccer team played 160 games and won 65 percent of them . how many games did it win ?

Explanation: "65 % of 160 = x 0.65 * 160 = x 104 = x answer : c"

<gadget id="calculator">65 * 160</gadget>
<output>10_400</output>
<gadget id="calculator">10_400 / 100</gadget>
<output>104</output>
<result>104</result>


a trader sells 80 meters of cloth for rs . 9000 at the profit of rs . 23.5 per metre of cloth . what is the cost price of one metre of cloth ?

Explanation: "sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b"

<gadget id="calculator">9_000 / 80</gadget>
<output>225/2 = around 112.5</output>
<gadget id="calculator">(225/2) - 23.5</gadget>
<output>89</output>
<result>89</result>


a farm has chickens , cows and sheep . there are 6 times the number of chickens and cows than sheep . if there are more cows than chickens or sheep , and together , cows and chickens have a total of 100 feet and heads , how many sheep live at the farm ?

Explanation: chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d

<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<result>4</result>


in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 75 percent of the registered voters who are democrats and 25 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?

Explanation: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a , which is 55 % of the total number of registered voters . answer : d ."

add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(25, const_100)))

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">60 * (3/4)</gadget>
<output>45</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">40 * (1/4)</gadget>
<output>10</output>
<gadget id="calculator">45 + 10</gadget>
<output>55</output>
<result>55</result>


a rower can row 5 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?

Explanation: "let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ."

multiply(divide(subtract(5, 2), add(add(5, 2), subtract(5, 2))), add(5, 2))

<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 7</gadget>
<output>21/10 = around 2.1</output>
<result>21/10 = around 2.1</result>


a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 24 m * 2 m * 0.75 m ?

Explanation: "24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c"

divide(divide(divide(multiply(multiply(multiply(24, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)

<gadget id="calculator">24 * 100</gadget>
<output>2_400</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">2_400 * 200</gadget>
<output>480_000</output>
<gadget id="calculator">0.75 * 100</gadget>
<output>75</output>
<gadget id="calculator">480_000 * 75</gadget>
<output>36_000_000</output>
<gadget id="calculator">36_000_000 / 20</gadget>
<output>1_800_000</output>
<gadget id="calculator">1_800_000 / 10</gadget>
<output>180_000</output>
<gadget id="calculator">180_000 / 7.5</gadget>
<output>24_000</output>
<result>24_000</result>


in a group of ducks and cows , the total number of legs are 28 more than twice the no . of heads . find the total no . of buffaloes .

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c"

<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>14</result>


a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 26 per kg , then his gain percent is

Explanation: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b"

divide(multiply(subtract(multiply(26, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">26 * 8</gadget>
<output>208</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">208 - 150</gadget>
<output>58</output>
<gadget id="calculator">58 * 100</gadget>
<output>5_800</output>
<gadget id="calculator">5_800 / 150</gadget>
<output>116/3 = around 38.666667</output>
<result>116/3 = around 38.666667</result>


joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 4 of the remaining paint . how many gallons of paint has joe used ?

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b"

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 4))

<gadget id="calculator">360 / 4</gadget>
<output>90</output>
<gadget id="calculator">90 * 1</gadget>
<output>90</output>
<gadget id="calculator">360 - 90</gadget>
<output>270</output>
<gadget id="calculator">270 / 4</gadget>
<output>135/2 = around 67.5</output>
<gadget id="calculator">90 + (135/2)</gadget>
<output>315/2 = around 157.5</output>
<result>315/2 = around 157.5</result>


a man has some hens and cows . if the number of heads be 50 and the number of feet equals 160 , then the number of hens will be :

Explanation: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d"

divide(subtract(multiply(50, const_4), 160), const_2)

<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">200 - 160</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


if a population of women in a town is 50 % of men . what is the population of men as a percentage of population of women ?

Explanation: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c"

<gadget id="calculator">100 / 50</gadget>
<output>2</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<result>200</result>


how many even multiples of 65 are there between 649 and 1301 ?

Explanation: "650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."

add(divide(subtract(1301, 649), multiply(65, const_2)), const_1)

<gadget id="calculator">1_301 - 649</gadget>
<output>652</output>
<gadget id="calculator">65 * 2</gadget>
<output>130</output>
<gadget id="calculator">652 / 130</gadget>
<output>326/65 = around 5.015385</output>
<gadget id="calculator">(326/65) + 1</gadget>
<output>391/65 = around 6.015385</output>
<result>391/65 = around 6.015385</result>


two trains are moving in opposite directions with speed of 70 km / hr and 90 km / hr respectively . their lengths are 1.10 km and 0.9 km respectively . the slower train cross the faster train in - - - seconds

Explanation: "explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b"

<gadget id="calculator">1.1 + 0.9</gadget>
<output>2</output>
<gadget id="calculator">70 + 90</gadget>
<output>160</output>
<gadget id="calculator">2 / 160</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">(1/80) * 3_600</gadget>
<output>45</output>
<result>45</result>


in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?

Explanation: "0,08 r = x / 100 * 0.1 r answer a"

multiply(divide(multiply(subtract(const_1, divide(20, const_100)), divide(10, const_100)), divide(10, const_100)), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(4/5) * (1/10)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) / (1/10)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>


if ( 2 to the x ) - ( 2 to the ( x - 2 ) ) = 3 ( 2 to the 5 ) , what is the value of x ?

Explanation: "( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a"

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


in an examination , the percentage of students qualified to the students appeared from school ' p ' is 70 % . in school ' q ' , the number of students appeared is 30 % more than the students appeared from school ' p ' and the number of students qualified from school ' q ' is 50 % more than the students qualified from school ' p ' . what is the % of students qualified to the number of students appeared from school ' q ' ?

Explanation: explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b

multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100)

<gadget id="calculator">50 + 100</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(3/2) * (7/10)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(21/20) / (13/10)</gadget>
<output>21/26 = around 0.807692</output>
<gadget id="calculator">(21/26) * 100</gadget>
<output>1_050/13 = around 80.769231</output>
<result>1_050/13 = around 80.769231</result>


there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 75 . how tall is the fourth person ?

Explanation: let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e .

add(divide(subtract(multiply(75, 4), add(6, add(4, 6))), 4), add(4, 6))

<gadget id="calculator">75 * 4</gadget>
<output>300</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">6 + 10</gadget>
<output>16</output>
<gadget id="calculator">300 - 16</gadget>
<output>284</output>
<gadget id="calculator">284 / 4</gadget>
<output>71</output>
<gadget id="calculator">71 + 10</gadget>
<output>81</output>
<result>81</result>


if the angles of an n sided polygon are in a . p and a > = 20 and d > = 20 then wat is the maximum possible value of n ?

Explanation: sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ( n + 1 ) = ( n − 2 ) 180 n = 14.52 since number of sides must be a positive integer , maximum value of n = 14 answer : b

divide(add(sqrt(subtract(power(subtract(20, const_3), const_2), multiply(const_4, multiply(divide(add(multiply(const_10, multiply(const_4, const_2)), const_100), const_10), const_2)))), subtract(20, const_3)), const_2)

<gadget id="calculator">20 - 3</gadget>
<output>17</output>
<gadget id="calculator">17 ** 2</gadget>
<output>289</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">80 + 100</gadget>
<output>180</output>
<gadget id="calculator">180 / 10</gadget>
<output>18</output>
<gadget id="calculator">18 * 2</gadget>
<output>36</output>
<gadget id="calculator">4 * 36</gadget>
<output>144</output>
<gadget id="calculator">289 - 144</gadget>
<output>145</output>
<gadget id="calculator">145 ** (1/2)</gadget>
<output>sqrt(145) = around 12.041595</output>
<gadget id="calculator">(sqrt(145)) + 17</gadget>
<output>sqrt(145) + 17 = around 29.041595</output>
<gadget id="calculator">(sqrt(145) + 17) / 2</gadget>
<output>sqrt(145)/2 + 17/2 = around 14.520797</output>
<result>sqrt(145)/2 + 17/2 = around 14.520797</result>


if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 82 ?

Explanation: "four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d"

<gadget id="calculator">82 - 2</gadget>
<output>80</output>
<gadget id="calculator">80 / 4</gadget>
<output>20</output>
<result>20</result>


if 50 % of x is 25 less than 25 % of 2500 , then x is ?

Explanation: "50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c"

divide(subtract(multiply(2500, divide(25, const_100)), 25), divide(50, const_100))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2_500 * (1/4)</gadget>
<output>625</output>
<gadget id="calculator">625 - 25</gadget>
<output>600</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">600 / (1/2)</gadget>
<output>1_200</output>
<result>1_200</result>


a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?

Explanation: "30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc"

divide(multiply(30, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))

<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">30 * (3/5)</gadget>
<output>18</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">18 / (2/5)</gadget>
<output>45</output>
<result>45</result>


in an examination , 30 % of total students failed in hindi , 35 % failed in english and 35 % in both . the percentage of these who passed in both the subjects is :

Explanation: "pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d"

subtract(const_100, subtract(add(30, 35), 35))

<gadget id="calculator">30 + 35</gadget>
<output>65</output>
<gadget id="calculator">65 - 35</gadget>
<output>30</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<result>70</result>


in a shop , the profit is 320 % of the cost . if the cost increases by 25 % but the selling price remains constant , find out approximately what percentage of the selling price is the profit ?

Explanation: let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e

multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100)

<gadget id="calculator">320 + 100</gadget>
<output>420</output>
<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">420 - 125</gadget>
<output>295</output>
<gadget id="calculator">295 / 420</gadget>
<output>59/84 = around 0.702381</output>
<gadget id="calculator">(59/84) * 100</gadget>
<output>1_475/21 = around 70.238095</output>
<result>1_475/21 = around 70.238095</result>


a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 10 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :

Explanation: total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a

<gadget id="calculator">1_200 * 100</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 10</gadget>
<output>12_000</output>
<result>12_000</result>


the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?

Explanation: "explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b"

<gadget id="calculator">12_000 - 8_000</gadget>
<output>4_000</output>
<gadget id="calculator">7 * 4_000</gadget>
<output>28_000</output>
<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>
<gadget id="calculator">28_000 / 2_000</gadget>
<output>14</output>
<gadget id="calculator">7 + 14</gadget>
<output>21</output>
<result>21</result>


a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 108 . what was the number he chose ?

Explanation: "let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a"

<gadget id="calculator">108 + 138</gadget>
<output>246</output>
<gadget id="calculator">246 / 2</gadget>
<output>123</output>
<result>123</result>


Explanation: "30 * 18 / 5 = 108 kmph answer : b"

<gadget id="calculator">30 / 1_000</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(3/100) * 3_600</gadget>
<output>108</output>
<result>108</result>


in a group of ducks and cows , the total number of legs are 8 more than twice the no . of heads . find the total no . of buffaloes .

Explanation: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b"

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


if log 8 x + log 8 1 / 6 = 1 / 3 , then the value of x is :

Explanation: "log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a"

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<result>12</result>


if the sum of two numbers is 12 and the sum of their squares is 124 , then the product of the numbers is

Explanation: "sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a"

divide(subtract(power(12, const_2), 124), const_2)

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">144 - 124</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>


the ratio between the sale price and the cost price of an article is 8 : 5 . what is the ratio between the profit and the cost price of that article ?

Explanation: "c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d"

<gadget id="calculator">8 - 5</gadget>
<output>3</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 9 even numbers . his mother immediately worked out the answer . how much had he scored in math ?

Explanation: "b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90"

<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">10 * 9</gadget>
<output>90</output>
<result>90</result>


out of 400 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?

Explanation: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b"

<gadget id="calculator">175 + 325</gadget>
<output>500</output>
<gadget id="calculator">400 - 50</gadget>
<output>350</output>
<gadget id="calculator">500 - 350</gadget>
<output>150</output>
<result>150</result>


50 men shake hands with each other . maximum no of handshakes without cyclic handshakes .

Explanation: total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c

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

<gadget id="calculator">50 - 1</gadget>
<output>49</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">49 * 25</gadget>
<output>1_225</output>
<result>1_225</result>


if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 10 minutes ?

Explanation: "since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ."

<gadget id="calculator">60 / 15</gadget>
<output>4</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<result>40</result>


if p ( a ) = 3 / 5 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .

Explanation: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a"

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(3/5) * (2/5)</gadget>
<output>6/25 = around 0.24</output>
<result>6/25 = around 0.24</result>


if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 3 flips and not on the last 2 flips ?

Explanation: "on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e"

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 5</gadget>
<output>1/32 = around 0.03125</output>
<result>1/32 = around 0.03125</result>


if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value q of z - x ?

Explanation: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d"

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<result>9</result>


a piece of work can finish by a certain number of men in 100 days . if however , there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?

Explanation: originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d

divide(multiply(divide(add(100, 10), 10), 10), subtract(divide(add(100, 10), 10), 10))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 10</gadget>
<output>11</output>
<gadget id="calculator">11 * 10</gadget>
<output>110</output>
<gadget id="calculator">11 - 10</gadget>
<output>1</output>
<gadget id="calculator">110 / 1</gadget>
<output>110</output>
<result>110</result>


how many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph ?

Explanation: d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec

<gadget id="calculator">200 + 150</gadget>
<output>350</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>
<gadget id="calculator">350 / 15</gadget>
<output>70/3 = around 23.333333</output>
<result>70/3 = around 23.333333</result>


an error 6 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?

Explanation: "percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e"

divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100))

<gadget id="calculator">100 + 6</gadget>
<output>106</output>
<gadget id="calculator">106 ** 2</gadget>
<output>11_236</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">11_236 - 10_000</gadget>
<output>1_236</output>
<gadget id="calculator">1_236 * 100</gadget>
<output>123_600</output>
<gadget id="calculator">123_600 / 10_000</gadget>
<output>309/25 = around 12.36</output>
<result>309/25 = around 12.36</result>


liz drove from point a to point b at 40 km / h . on her way back she drove at 50 km / h and therefore her way back lasted one hour less . what is the distance ( in km ) between a and b ?

Explanation: distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b

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

<gadget id="calculator">50 - 40</gadget>
<output>10</output>
<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 * 40</gadget>
<output>200</output>
<result>200</result>


the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 60 percent of b , what is the value of m / x ?

Explanation: "a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ."

multiply(divide(subtract(const_100, 60), add(const_100, 75)), divide(5, 4))

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">40 / 175</gadget>
<output>8/35 = around 0.228571</output>
<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(8/35) * (5/4)</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>


in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 700 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 2,100 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?

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

divide(multiply(700, const_100), add(add(multiply(const_2, const_1000), const_100), 700))

<gadget id="calculator">700 * 100</gadget>
<output>70_000</output>
<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 + 100</gadget>
<output>2_100</output>
<gadget id="calculator">2_100 + 700</gadget>
<output>2_800</output>
<gadget id="calculator">70_000 / 2_800</gadget>
<output>25</output>
<result>25</result>


the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 8 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?

Explanation: "actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b"

<gadget id="calculator">480 / 40</gadget>
<output>12</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<result>4</result>


a square is drawn inside a right - angled triangle with the two perpendicular sides as 12 cm and 8 cm . what is the side of the largest possible square that can be drawn ?

Explanation: area of triangle is 1 / 2 * 12 * 8 = 48 side of square = x the entire triangle split into two right angled triangle and one square with dimensions as follows i ) square with side x ii ) right angled triangle with perpendicular sides x and 12 - x iii ) right angled triangle with perpendicular sides 8 - x and x sum of area of all three = 48 = x 2 + 1 / 2 * x * ( 12 - x ) + 1 / 2 * x * ( 8 - x ) = 48 = x = 4.8 cm answer : a

divide(divide(multiply(12, 8), const_2), const_10)

<gadget id="calculator">12 * 8</gadget>
<output>96</output>
<gadget id="calculator">96 / 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 10</gadget>
<output>24/5 = around 4.8</output>
<result>24/5 = around 4.8</result>


the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be social teachers ?

Explanation: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( b )"

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

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) * (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<result>1/12 = around 0.083333</result>


in a 160 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :

Explanation: b runs 56 m in 7 sec . = > b runs 160 m in 7 / 56 * 160 = 20 seconds since a beats b by 7 seconds , a runs 160 m in ( 20 - 7 ) = 13 seconds hence , a ' s time over the course = 13 seconds answer : c

subtract(multiply(divide(7, 56), 160), 7)

<gadget id="calculator">7 / 56</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 160</gadget>
<output>20</output>
<gadget id="calculator">20 - 7</gadget>
<output>13</output>
<result>13</result>


by how much is 70 % of 120 greater than 35 % of 200 .

Explanation: ( 70 / 100 ) * 120 â € “ ( 35 / 100 ) * 200 84 - 70 = 14 answer : b

subtract(multiply(120, divide(70, const_100)), multiply(divide(35, const_100), 200))

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">120 * (7/10)</gadget>
<output>84</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 200</gadget>
<output>70</output>
<gadget id="calculator">84 - 70</gadget>
<output>14</output>
<result>14</result>


in 10 years , a will be twice as old 5 as b was 10 years ago . if a is now 5 years older than b , the present age of b is

Explanation: "explanation : let b ' s age = x years . then , as age = ( x + 5 ) years . ( x + 5 + 10 ) = 2 ( x — 10 ) hence x = 35 . present age of b = 35 years answer : option a"

<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<result>35</result>


Explanation: "2 ^ 3 + 7 ^ 2 = 57 3 ^ 3 + 6 ^ 2 = 63 5 ^ 3 + 9 ^ 2 = 206 and 5 ^ 3 + 8 ^ 2 = 189 answer : e"

<gadget id="calculator">5 ** 3</gadget>
<output>125</output>
<gadget id="calculator">8 ** 2</gadget>
<output>64</output>
<gadget id="calculator">125 + 64</gadget>
<output>189</output>
<result>189</result>


if a man lost 7 % by selling oranges at the rate of 21 a rupee at how many a rupee must he sell them to gain 42 % ?

Explanation: "93 % - - - - 21 142 % - - - - ? 93 / 142 * 21 = 13.75 answer : e"

divide(multiply(subtract(const_100, 7), 21), add(const_100, 42))

<gadget id="calculator">100 - 7</gadget>
<output>93</output>
<gadget id="calculator">93 * 21</gadget>
<output>1_953</output>
<gadget id="calculator">100 + 42</gadget>
<output>142</output>
<gadget id="calculator">1_953 / 142</gadget>
<output>1_953/142 = around 13.753521</output>
<result>1_953/142 = around 13.753521</result>


a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.4 m and its walls are 5 cm thick . the thickness of the bottom is :

Explanation: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 140 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 140 - x ) = 8000 × 1000 = > ( 140 - x ) = 8000 × 1000 / 320 = 100 = > x = 40 cm = 4 dm . answer : b"

subtract(multiply(multiply(3.3, 2.6), 1.4), divide(8000, const_1000))

<gadget id="calculator">3.3 * 2.6</gadget>
<output>8.58</output>
<gadget id="calculator">8.58 * 1.4</gadget>
<output>12.012</output>
<gadget id="calculator">8_000 / 1_000</gadget>
<output>8</output>
<gadget id="calculator">12.012 - 8</gadget>
<output>4.012</output>
<result>4.012</result>


a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 16 days . in how many days b alone can do the work ?

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 16 x = 24 days answer : option d"

inverse(multiply(inverse(16), subtract(const_1, multiply(5, inverse(15)))))

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">5 * (1/15)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/16) * (2/3)</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">1 / (1/24)</gadget>
<output>24</output>
<result>24</result>


a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length .

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds answer : d"

divide(add(360, 140), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">360 + 140</gadget>
<output>500</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">500 / (25/2)</gadget>
<output>40</output>
<result>40</result>


if a 2 - b 2 = 9 and a * b = 4 , find a 4 + b 4 .

Explanation: "a 2 - b 2 = 9 : given a 4 + b 4 - 2 a 2 b 2 = 92 : square both sides and expand . a * b = 4 : given a 2 b 2 = 42 : square both sides . a 4 + b 4 - 2 ( 16 ) = 81 : substitute a 4 + b 4 = 113 correct answer c"

add(power(9, 2), multiply(power(4, 2), 2))

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 2</gadget>
<output>32</output>
<gadget id="calculator">81 + 32</gadget>
<output>113</output>
<result>113</result>


a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 15 % salt solution . what is the value of x ?

Explanation: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 15 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 15 ) / ( 15 - 0 ) = 7 / 3 1 / x = 7 / 3 x = 3 / 7 answer : e"

<gadget id="calculator">50 - 15</gadget>
<output>35</output>
<gadget id="calculator">15 / 35</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>


the cyclist going at a constant rate of 18 miles per hour is passed by a motor - cyclist traveling in the same direction along the same path at 48 miles per hour . the motor - cyclist stops to wait for the cyclist 15 minutes after passing cyclist , while the cyclist continues to travel at constant rate , how many minutes must the motor - cyclist wait until the cyclist catches up ?

Explanation: for the 15 minutes the motor - cyclist continues to overtake the cyclist , she is going at 30 miles per hour faster than the cyclist . once the motor - cyclist stops , the cyclist is going at 18 miles per hour while the motor - cyclist is at rest so the amount of time the cyclist will take to cover the distance between them is going to be in the ratio of the relative speeds . 30 / 18 * 15 or 25 minutes answer is ( a )

divide(multiply(subtract(divide(48, const_4), divide(18, const_4)), const_60), 18)

<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<gadget id="calculator">18 / 4</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">12 - (9/2)</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) * 60</gadget>
<output>450</output>
<gadget id="calculator">450 / 18</gadget>
<output>25</output>
<result>25</result>


a number is doubled and 9 is added . if the resultant is trebled , it becomes 81 . what is that number ?

Explanation: "let the number be x . then , 3 ( 2 x + 9 ) = 81 2 x = 18 = > x = 9 answer : e"

divide(subtract(81, multiply(const_3, 9)), multiply(const_3, const_2))

<gadget id="calculator">3 * 9</gadget>
<output>27</output>
<gadget id="calculator">81 - 27</gadget>
<output>54</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">54 / 6</gadget>
<output>9</output>
<result>9</result>


in a renowned city , the average birth rate is 9 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .

Explanation: "every 2 seconds , 6 persons are added ( 9 - 3 ) . every second 3 persons are added . in a day 24 hrs = 24 * 60 minutes = 24 * 60 * 60 = 86400 seconds . 86400 * 3 = 259200 option e"

multiply(multiply(subtract(9, 3), const_3600), const_12)

<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 3_600</gadget>
<output>21_600</output>
<gadget id="calculator">21_600 * 12</gadget>
<output>259_200</output>
<result>259_200</result>


the squared value of the diagonal of a rectangle is ( 64 + b 2 ) sq cm , where b is less than 8 cm . what is the breadth of that rectangle ?

Explanation: diagonal 2 = 64 + b 2 or , 10 ( 2 ) = 64 + 6 ( 2 ) answer a

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<result>6</result>


the cost price of 60 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?

Explanation: "let the cost price = y the cost price of 60 articles = 60 y the selling price of x articles = 1.20 y * x 1.20 y * x = 60 y x = 60 / 1.2 = 50 the answer is d ."

divide(multiply(60, const_4), add(const_4, const_1))

<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>


on a certain transatlantic crossing , 40 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 20 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?

Explanation: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.4 t had round trip tickets and took their cars . 0.8 x had round trip tickets and took their cars . 0.8 x = 0.4 t x = 0.5 t the answer is c ."

divide(40, subtract(const_1, divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">40 / (4/5)</gadget>
<output>50</output>
<result>50</result>


in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?

Explanation: 30 , 870,000 = 2 ^ 4 * 5 ^ 4 * 3087 = 2 ^ 4 * 3 * 5 ^ 4 * 1029 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 343 = 2 ^ 4 * 3 ^ 2 * 5 ^ 4 * 7 ^ 3 the answer is c .

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


# 88 a necklace is made by stringing q no individual beads together in the repeating pattern red bead , green bead , white bead , blue bead , and yellow bead . if the necklace design begins with a red bead and ends with a white bead , then q could equal

Explanation: you can just write out the pattern and count : rgwbyrgwbyrgwby . . . but to save time a good test taker will just look for a pattern . min # is 3 , because w is the third one . then every 5 beads another white comes , so it must be 3 + 5 + 5 + 5 . . and so on . . . 3 + 5 = 8 3 + 5 + 5 = 13 3 + 5 + 5 + 5 = 18 3 + 5 + 5 + 5 + 5 = 23 so you see it ends in either 8 or 3 . pick an answer that ends in either 8 or 3 . only one answer does , b .

add(add(add(add(add(add(divide(88, 88), const_2), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3)), add(const_2, const_3))

<gadget id="calculator">88 / 88</gadget>
<output>1</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 5</gadget>
<output>13</output>
<gadget id="calculator">13 + 5</gadget>
<output>18</output>
<gadget id="calculator">18 + 5</gadget>
<output>23</output>
<gadget id="calculator">23 + 5</gadget>
<output>28</output>
<result>28</result>


a distributor sells a product through an online store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 16 per item . what is the price that the buyer observers online if the distributor wants to maintain a 20 % profit on the cost of the item ?

Explanation: let x be the price that buyers see online . the distributor wants to receive 1.2 ( original price ) which should be 80 % of x . 1.2 ( 16 ) = 0.8 x x = 1.2 ( 16 ) / 0.8 = 1.5 ( 16 ) = $ 24 the answer is e .

divide(add(multiply(divide(20, const_100), 16), 16), divide(subtract(const_100, 20), const_100))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 16</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(16/5) + 16</gadget>
<output>96/5 = around 19.2</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">(96/5) / (4/5)</gadget>
<output>24</output>
<result>24</result>


rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 3000 . then his monthly salary is

Explanation: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 3000 â ‡ ” 20 / 100 x = 3000 â ‡ ” x = 3000 ã — 5 = 15000 . answer a"

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">3_000 * 5</gadget>
<output>15_000</output>
<result>15_000</result>


last year a certain bond price with a face value of 5000 yielded 9 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?

Explanation: "interest = 0.09 * 5000 = 0.065 * selling price - - > selling price = 0.09 * 5000 / 0.065 - - > selling price = ~ 6,923 answer : e ."

divide(multiply(5000, divide(9, const_100)), divide(6.5, const_100))

<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">5_000 * (9/100)</gadget>
<output>450</output>
<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>
<gadget id="calculator">450 / 0.065</gadget>
<output>6_923.076923</output>
<result>6_923.076923</result>


a train of 40 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?

Explanation: d = 40 * 60 + 1500 = 3900 m t = 3900 / 60 * 18 / 5 = 234 sec = 3.9 mins answer : d

add(divide(multiply(add(40, const_1), 60), const_1000), 1.5)

<gadget id="calculator">40 + 1</gadget>
<output>41</output>
<gadget id="calculator">41 * 60</gadget>
<output>2_460</output>
<gadget id="calculator">2_460 / 1_000</gadget>
<output>123/50 = around 2.46</output>
<gadget id="calculator">(123/50) + 1.5</gadget>
<output>3.96</output>
<result>3.96</result>


Explanation: "given expression = ( 0.15 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.15 ) ( power 2 ) + ( 0.15 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.15 - 0.1 ) = 0.05 answer is c ."

<gadget id="calculator">0.15 ** 3</gadget>
<output>0.003375</output>
<gadget id="calculator">0.1 ** 3</gadget>
<output>0.001</output>
<gadget id="calculator">0.003375 - 0.001</gadget>
<output>0.002375</output>
<gadget id="calculator">0.15 ** 2</gadget>
<output>0.0225</output>
<gadget id="calculator">0.0225 + 0.015</gadget>
<output>0.0375</output>
<gadget id="calculator">0.1 ** 2</gadget>
<output>0.01</output>
<gadget id="calculator">0.0375 + 0.01</gadget>
<output>0.0475</output>
<gadget id="calculator">0.002375 / 0.0475</gadget>
<output>0.05</output>
<result>0.05</result>


a retailer sells 7 shirts . the first 2 he sells for $ 38 and $ 42 . if the retailer wishes to sell the 7 shirts for an overall average price of over $ 50 , what must be the minimum average price of the remaining 5 shirts ?

Explanation: first 2 shirts are sold for $ 38 and $ 42 = $ 80 . to get average price of $ 50 , total sale should be 7 * $ 50 = $ 350 so remaining 5 shirts to be sold for $ 350 - $ 80 = $ 270 answer should be 270 / 5 = $ 54.00 that is a

divide(subtract(multiply(7, 50), add(38, 42)), subtract(7, 2))

<gadget id="calculator">7 * 50</gadget>
<output>350</output>
<gadget id="calculator">38 + 42</gadget>
<output>80</output>
<gadget id="calculator">350 - 80</gadget>
<output>270</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">270 / 5</gadget>
<output>54</output>
<result>54</result>


a person crosses a 500 m long street in 4 minutes . what is his speed in km per hour ?

Explanation: "distance = 500 meter time = 4 minutes = 4 x 60 seconds = 240 seconds speed = distance / time = 500 / 240 = 2.08 m / s = 2.08 ã — 18 / 5 km / hr = 7.5 km / hr answer : a"

divide(divide(500, const_1000), divide(multiply(4, const_60), const_3600))

<gadget id="calculator">500 / 1_000</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 * 60</gadget>
<output>240</output>
<gadget id="calculator">240 / 3_600</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/2) / (1/15)</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>


if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 160 , how much more remains to be paid ?

Explanation: "10 / 100 p = 160 > > p = 160 * 100 / 10 = 1600 1600 - 160 = 1440 answer : e"

subtract(multiply(160, divide(const_100, 10)), 160)

<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">160 * 10</gadget>
<output>1_600</output>
<gadget id="calculator">1_600 - 160</gadget>
<output>1_440</output>
<result>1_440</result>


if the perimeter of a rectangular garden is 600 m , its length when its breadth is 100 m is ?

Explanation: "2 ( l + 100 ) = 600 = > l = 200 m answer : c"

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


you need to pick any number from ' 1 , 3 , 5 , 7 , 9 , 11 , 13 and 15 ' to make below equation true . ( ) + ( ) + ( ) = 30 can you solve it ?

Explanation: solution : 3 ! + 15 + 9 = 30 explanation : 3 ! = 3 * 2 * 1 = 6 6 + 15 + 9 = 30 answer b

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">11 + 6</gadget>
<output>17</output>
<gadget id="calculator">17 + 13</gadget>
<output>30</output>
<result>30</result>


ram and shyam start a two - length swimming race at the same moment but from opposite ends of the pool . they swim in lanes at uniform speeds , but hardy is faster than andy . they 1 st pass at a point 18.5 m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec . after setting off on the return length , the swimmers pass for the 2 nd time just 10.5 m from the shallow end . how long is the pool ?

Explanation: let x = length of pool at first meeting , combined distance = x at second meeting , combined distance = 3 x if andy swims 18.5 m of x , then he will swim 3 * 18.5 = 55.5 m of 3 x andy ' s total distance to second meeting = x + 10.5 m x + 10.5 = 55.5 m x = 45 m e

subtract(add(multiply(18.5, const_2), 18.5), 10.5)

<gadget id="calculator">18.5 * 2</gadget>
<output>37</output>
<gadget id="calculator">37 + 18.5</gadget>
<output>55.5</output>
<gadget id="calculator">55.5 - 10.5</gadget>
<output>45</output>
<result>45</result>


what least number must besubtracted from 427398 so that remaining no . is divisible by 15 ?

Explanation: on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted answer : option a

subtract(subtract(subtract(multiply(multiply(multiply(427398, const_100), const_10), const_2), 427398), multiply(427398, const_100)), multiply(multiply(multiply(const_100, const_100), const_100), const_100))


in covering a distance of 48 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :

Explanation: "let abhay ' s speed be x km / hr . then , 48 / x - 48 / 2 x = 3 6 x = 48 x = 8 km / hr . answer : option e"

divide(subtract(48, divide(48, 2)), add(1, 2))

<gadget id="calculator">48 / 2</gadget>
<output>24</output>
<gadget id="calculator">48 - 24</gadget>
<output>24</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<result>8</result>


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

Explanation: dist 1 st hr = 35 km speed of bus by 2 kmph 2 nd hr = 37 km 3 rd hr = 39 km tot = 35 + 37 + 39 + . . . . ( 12 terms ) 12 / 2 ( 2 * 35 + ( 12 - 1 ) 2 ] = 6 * 92 = 552 answer c

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

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


harkamal purchased 8 kg of grapes at the rate of 90 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

Explanation: "cost of 8 kg grapes = 90 × 8 = 720 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 720 + 495 = 1215 . b )"

<gadget id="calculator">8 * 90</gadget>
<output>720</output>
<gadget id="calculator">9 * 55</gadget>
<output>495</output>
<gadget id="calculator">720 + 495</gadget>
<output>1_215</output>
<result>1_215</result>


the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 16 terms of the arithmetic progression ?

Explanation: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 16 . . . we get 15 / 2 [ 2 a + 14 d ] = 16 [ a + 7 d ] = 16 * 10 = 160 . . . answer is d . . ."

<gadget id="calculator">20 * 16</gadget>
<output>320</output>
<gadget id="calculator">320 / 2</gadget>
<output>160</output>
<result>160</result>


there are 3 red shoes & 7 green shoes . if two of red shoes are drawn what is the probability of getting red shoes

Explanation: "taking 2 red shoe the probablity is 3 c 2 from 10 shoes probablity of taking 2 red shoe is 3 c 2 / 10 c 2 = 1 / 15 answer : d"

divide(choose(3, const_2), choose(add(3, 7), const_2))

<gadget id="calculator">binomial(3, 2)</gadget>
<output>3</output>
<gadget id="calculator">3 + 7</gadget>
<output>10</output>
<gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>
<gadget id="calculator">3 / 45</gadget>
<output>1/15 = around 0.066667</output>
<result>1/15 = around 0.066667</result>


it will take 16 days for mary to complete a certain task alone . she worked for 8 days before she was joined by her sister . both of them completed the remaining task in 2 and half days . if her sister had joined her when she started the task , how many days would it have taken ?

Explanation: explanation : mary and her sister complete half work in 2.5 days = > they can complete whole work in 5 days answer : option d

add(divide(divide(const_1, 8), divide(const_1, 16)), const_3)

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/8) / (1/16)</gadget>
<output>2</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<result>5</result>


on dividing 73 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?

Explanation: "d = ( d - r ) / q = ( 73 - 1 ) / 9 = 72 / 9 = 8 a )"

<gadget id="calculator">73 / 9</gadget>
<output>73/9 = around 8.111111</output>
<gadget id="calculator">floor(73/9)</gadget>
<output>8</output>
<result>8</result>


shruti purchased several number of 3 articles p , q and r in the proportion 3 : 2 : 3 . if the unit costs of the articles p , q and r are 200 , rs . 90 and rs . 60 respectively , how many articles of q must have been purchased in the total purchases of rs . 4800 ?

Explanation: explanation : let the number of articles of types p , q and r be 3 a , 2 a and 3 a respectively . thus , we get , ( 200 x 3 a ) + ( 90 x 2 a ) + ( 60 x 3 a ) = 4800 960 a = 4800 a = 5 hence , the number of articles of type “ q ” = 2 x 5 = 10 answer b

multiply(divide(4800, add(add(multiply(3, 200), multiply(2, 90)), multiply(3, 60))), 2)

<gadget id="calculator">3 * 200</gadget>
<output>600</output>
<gadget id="calculator">2 * 90</gadget>
<output>180</output>
<gadget id="calculator">600 + 180</gadget>
<output>780</output>
<gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">780 + 180</gadget>
<output>960</output>
<gadget id="calculator">4_800 / 960</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<result>10</result>


a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 9 are wrong and the other digits are correct , then the correct answer would be :

Explanation: 987 = 3 x 7 x 47 so , the required number must be divisible by each one of 3 , 7 , 47 553681 - > ( sum of digits = 28 , not divisible by 3 ) 555181 - > ( sum of digits = 25 , not divisible by 3 ) 555681 is divisible by 3 , 7 , 47 answer c

multiply(subtract(subtract(divide(559981, 987), const_4), const_0_33), 987)


the least number which when increased by 5 each divisible by each one of 24 , 32 , 36 and 54 is :

Explanation: solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 5 = 859 . answer b

<gadget id="calculator">lcm(24, 32)</gadget>
<output>96</output>
<gadget id="calculator">lcm(96, 36)</gadget>
<output>288</output>
<gadget id="calculator">lcm(288, 54)</gadget>
<output>864</output>
<gadget id="calculator">864 - 5</gadget>
<output>859</output>
<result>859</result>


a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

Explanation: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 140 ) / 140 = 40 / 140 = 2 / 7 = ~ 29 % . answer : e ."

multiply(divide(subtract(add(const_1, divide(80, const_100)), add(const_1, divide(40, const_100))), add(const_1, divide(40, const_100))), const_100)

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 + (4/5)</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(9/5) - (7/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) / (7/5)</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">(2/7) * 100</gadget>
<output>200/7 = around 28.571429</output>
<result>200/7 = around 28.571429</result>


if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 65 , what is the common ratio of the g . p ?

Explanation: 65 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 65 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 65 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 64 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 64 = r ^ 3 r = 4 a

power(subtract(65, const_1), divide(const_1, const_3))

<gadget id="calculator">65 - 1</gadget>
<output>64</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<result>4</result>


when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 1 / 3 of the remaining balance , what will be the final balance in her bank account ?

Explanation: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 1 / 3 of 300 = 100 total amount in her account = 400 answer c"

multiply(subtract(divide(200, subtract(1, divide(const_3, 5))), 200), add(1, divide(1, 3)))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<gadget id="calculator">500 - 200</gadget>
<output>300</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">300 * (4/3)</gadget>
<output>400</output>
<result>400</result>


a man traveled a total distance of 1200 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ?

Explanation: total distance traveled = 1200 km . distance traveled by plane = 400 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 400 = 1200 5 x / 3 = 800 x = 480 km the answer is c .

divide(multiply(divide(multiply(1200, const_2), const_3), const_3), add(const_2, const_3))

<gadget id="calculator">1_200 * 2</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 3</gadget>
<output>800</output>
<gadget id="calculator">800 * 3</gadget>
<output>2_400</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2_400 / 5</gadget>
<output>480</output>
<result>480</result>


in town x , 64 percent of the population are employed , and 40 percent of the population are employed males . what percent of the employed people in town x are females ?

Explanation: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 40 are employed males , hence 24 % are employed females . ( employed females ) / ( total employed people ) = 24 / 64 = 38 % answer : a ."

multiply(divide(subtract(64, 40), 64), const_100)

<gadget id="calculator">64 - 40</gadget>
<output>24</output>
<gadget id="calculator">24 / 64</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/8) * 100</gadget>
<output>75/2 = around 37.5</output>
<result>75/2 = around 37.5</result>


a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 237 for it , the cost price of the cricket bat for a is :

Explanation: "125 % of 120 % of a = 237 125 / 100 * 120 / 100 * a = 237 a = 237 * 2 / 3 = 158 . answer c"

divide(237, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100))))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(6/5) * (5/4)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">237 / (3/2)</gadget>
<output>158</output>
<result>158</result>


how many numbers between 100 and 756 are divisible by 2 , 3 , and 7 together ?

Explanation: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 756 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 756 : 756 / 42 = 18 hence , 42 * 16 = 756 is the last number divisible by 42 within 756 hence , total numbers divisible by 2 , 3 , 7 together are ( 18 â € “ 2 ) = 16 answer : d"

subtract(divide(756, multiply(multiply(2, 3), 7)), divide(100, multiply(multiply(2, 3), 7)))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">756 / 42</gadget>
<output>18</output>
<gadget id="calculator">100 / 42</gadget>
<output>50/21 = around 2.380952</output>
<gadget id="calculator">18 - (50/21)</gadget>
<output>328/21 = around 15.619048</output>
<result>328/21 = around 15.619048</result>


if the sides of a cube are in the ratio 9 : 5 . what is the ratio of their diagonals ?

Explanation: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 5 d 1 : d 2 = 9 : 5 where √ 3 cancelled both side answer : a"

<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>


a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . so a , b and c together finish same work in how many days ?

Explanation: ( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 so , all three together finish work in 10 days answer d

inverse(divide(add(inverse(12), add(inverse(20), inverse(15))), const_2))

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/20) + (1/15)</gadget>
<output>7/60 = around 0.116667</output>
<gadget id="calculator">(1/12) + (7/60)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / 2</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / (1/10)</gadget>
<output>10</output>
<result>10</result>


if a train , travelling at a speed of 180 kmph , crosses a pole in 6 sec , then the length of train is ?

Explanation: d = 180 * 5 / 18 * 6 = 300 m answer : a

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">180 * (5/18)</gadget>
<output>50</output>
<gadget id="calculator">50 * 6</gadget>
<output>300</output>
<result>300</result>


a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 36 . find the profit percentage ?

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 180 ( 36 * 5 ) profit percentage = ( 180 - 100 ) / 100 * 100 = 80 % answer : a"

subtract(multiply(36, add(const_4, const_1)), multiply(25, const_4))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">36 * 5</gadget>
<output>180</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">180 - 100</gadget>
<output>80</output>
<result>80</result>