what is the greatest of 3 consecutive integers whose sum is 30 ?

Explanation: "30 / 3 = 10 the three numbers are 9 , 10 , and 11 . the answer is d ."

add(divide(subtract(30, 3), 3), const_2)

<gadget id="calculator">30 - 3</gadget>
<output>27</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 2</gadget>
<output>11</output>
<result>11</result>


students of 3 different classes appeared in common examination . pass average of 10 students of first class was 45 % , pass average of 15 students of second class was 60 % and pass average of 25 students of third class was 80 % then what will be the pass average of all students of 3 classes ?

Explanation: solution : sum of pass students of first , second and third class , = ( 45 % of 10 ) + ( 60 % of 15 ) + ( 80 % of 25 ) = 4.5 + 9 + 20 = 33.5 total students appeared , = 10 + 15 + 25 = 50 pass average , = 33.5 * 100 / 50 = 67 % . answer : option c

divide(multiply(add(add(divide(multiply(10, 45), const_100), divide(multiply(15, 60), const_100)), divide(multiply(25, 80), const_100)), const_100), add(add(10, 15), 25))

<gadget id="calculator">10 * 45</gadget>
<output>450</output>
<gadget id="calculator">450 / 100</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">15 * 60</gadget>
<output>900</output>
<gadget id="calculator">900 / 100</gadget>
<output>9</output>
<gadget id="calculator">(9/2) + 9</gadget>
<output>27/2 = around 13.5</output>
<gadget id="calculator">25 * 80</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">(27/2) + 20</gadget>
<output>67/2 = around 33.5</output>
<gadget id="calculator">(67/2) * 100</gadget>
<output>3_350</output>
<gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<gadget id="calculator">3_350 / 50</gadget>
<output>67</output>
<result>67</result>


if the sides of a triangle are 20 cm , 12 cm and 16 cm , what is its area ?

Explanation: "the triangle with sides 20 cm , 12 cm and 16 cm is right angled , where the hypotenuse is 20 cm . area of the triangle = 1 / 2 * 12 * 16 = 96 cm 2 answer : option d"

<gadget id="calculator">12 * 16</gadget>
<output>192</output>
<gadget id="calculator">192 / 2</gadget>
<output>96</output>
<result>96</result>


how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

Explanation: "d = 100 + 150 = 250 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 25 sec . answer : c"

<gadget id="calculator">150 + 100</gadget>
<output>250</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">250 / 10</gadget>
<output>25</output>
<result>25</result>


Explanation: 34.94 240.016 + 23.98 - - - - - - - - 298.936 answer is a .

<gadget id="calculator">34.94 + 240.016</gadget>
<output>274.956</output>
<gadget id="calculator">274.956 + 23.98</gadget>
<output>298.936</output>
<result>298.936</result>


meera purchased two 3 items from a shop . total price for 3 items is rs . 2000 / - she have given rs . 3000 / - what is the balance amount meera got ?

Explanation: total cost of items : 2000 / - amount paid : 3000 / - balance receivable : 3000 - 2000 = 1000 / - answer is b

<gadget id="calculator">3_000 - 2_000</gadget>
<output>1_000</output>
<result>1_000</result>


a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 36 instead of 86 then find the correct average marks up to two decimal places .

Explanation: "correct average = 35 x 72 + ( 86 - 36 ) / 35 ≈ 72 + 1.43 = 73.43 answer d"

divide(subtract(multiply(35, 72), subtract(86, 36)), 35)

<gadget id="calculator">35 * 72</gadget>
<output>2_520</output>
<gadget id="calculator">86 - 36</gadget>
<output>50</output>
<gadget id="calculator">2_520 - 50</gadget>
<output>2_470</output>
<gadget id="calculator">2_470 / 35</gadget>
<output>494/7 = around 70.571429</output>
<result>494/7 = around 70.571429</result>


what is the smallest integer e greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?

Explanation: or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder e as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 68 and 10 is 121 . c

<gadget id="calculator">lcm(6, 8)</gadget>
<output>24</output>
<gadget id="calculator">lcm(10, 24)</gadget>
<output>120</output>
<gadget id="calculator">120 + 1</gadget>
<output>121</output>
<result>121</result>


a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 30 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 40 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .

Explanation: "anyways , one can infer that he ' steals ' 30 % from suppliers and then charges 40 % extra to customers so basically 1.3 * 1.4 = 1.82 given that 1 is start point , we get 21 % more hence answer is b"

subtract(multiply(divide(add(const_100, 40), const_100), add(const_100, 30)), const_100)

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">(7/5) * 130</gadget>
<output>182</output>
<gadget id="calculator">182 - 100</gadget>
<output>82</output>
<result>82</result>


in a class of 37 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?

Explanation: "26 + 20 - 17 = 29 37 - 29 = 8 play neither answer is b"

<gadget id="calculator">26 + 20</gadget>
<output>46</output>
<gadget id="calculator">46 - 17</gadget>
<output>29</output>
<gadget id="calculator">37 - 29</gadget>
<output>8</output>
<result>8</result>


a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 86 km downstream .

Explanation: "speed of boat in still water = 15 km / hr speed of the stream = 6 km / hr speed downstream = ( 15 + 6 ) = 21 km / hr time taken to travel 86 km downstream = 86 â  „ 16 = 17 â  „ 4 = 4.1 hours answer is a"

<gadget id="calculator">15 + 6</gadget>
<output>21</output>
<gadget id="calculator">86 / 21</gadget>
<output>86/21 = around 4.095238</output>
<result>86/21 = around 4.095238</result>


bhanu spends 30 % of his income on petrol on scooter 12 % of the remaining on house rent and the balance on food . if he spends rs . 300 on petrol then what is the expenditure on house rent ?

Explanation: given 30 % ( income ) = 300 ⇒ ⇒ income = 1000 after having spent rs . 300 on petrol , he left with rs . 700 . his spending on house rent = 12 % ( 700 ) = rs . 84 answer : c

multiply(subtract(divide(300, divide(30, const_100)), 300), divide(12, const_100))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">300 / (3/10)</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 300</gadget>
<output>700</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">700 * (3/25)</gadget>
<output>84</output>
<result>84</result>


a train running at a speed of 36 km / h passes an electric pole in 15 seconds . in how many seconds will the whole train pass a 370 - meter long platform ?

Explanation: "let the length of the train be x meters . when a train crosses an electric pole , the distance covered is its own length x . speed = 36 km / h = 36000 m / 3600 s = 10 m / s x = 15 * 10 = 150 m . the time taken to pass the platform = ( 150 + 370 ) / 10 = 52 seconds the answer is d ."

divide(add(multiply(multiply(36, const_0_2778), 15), 370), multiply(36, const_0_2778))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">10 * 15</gadget>
<output>150</output>
<gadget id="calculator">150 + 370</gadget>
<output>520</output>
<gadget id="calculator">520 / 10</gadget>
<output>52</output>
<result>52</result>


a pump can fill a tank with water in 3 hours . because of a leak , it took 3 1 / 3 hours to fill the tank . the leak can drain all the water of the tank in ?

Explanation: "work done by the tank in 1 hour = ( 1 / 3 - 3 1 / 3 ) = 1 / 30 leak will empty the tank in 30 hrs . answer : c"

inverse(subtract(divide(1, 3), inverse(divide(add(multiply(3, 3), 1), 3))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 + 1</gadget>
<output>10</output>
<gadget id="calculator">10 / 3</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">1 / (10/3)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/3) - (3/10)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>


from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 13 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?

Explanation: "soln : - 13 x = 45 - - > 87 / 77 * x = 45 - - > x = 45 * 77 / 87 = 677 / 17 = ~ 40 . answer : c ."

multiply(divide(const_100, add(const_100, 13)), 45)

<gadget id="calculator">100 + 13</gadget>
<output>113</output>
<gadget id="calculator">100 / 113</gadget>
<output>100/113 = around 0.884956</output>
<gadget id="calculator">(100/113) * 45</gadget>
<output>4_500/113 = around 39.823009</output>
<result>4_500/113 = around 39.823009</result>


ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio r of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?

Explanation: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio r of ann ' s time to bob ' s time is 3 : 2 . answer : b ."

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

<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">2 / (4/3)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


if ( a - b - c + d = 18 ) and ( a + b - c - d = 4 ) , what is the value of ( b - d ) ^ 2 ?

Explanation: "eq 1 : a - b - c + d = 18 eq 2 : a + b - c - d = 4 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 18 - a + b - c - d = 4 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 14 ( 2 ) simplify - b + d = 7 b - d = - 7 ( b - d ) ^ 2 = ( - 7 ) ^ 2 = 49 my answer : a"

power(subtract(4, divide(add(18, 4), 2)), 2)

<gadget id="calculator">18 + 4</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">4 - 11</gadget>
<output>-7</output>
<gadget id="calculator">(-7) ** 2</gadget>
<output>49</output>
<result>49</result>


john purchased some shirts and trousers for $ 800 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?

Explanation: given that the total purchase of two items cost 800 . so the average purchase of one item will cost 800 / 2 = 400 . its given as total shirt cost 400 $ less . hence total shirt cost = 400 - 200 and total trouser cost = 400 + 200 5 shirts = 200 $ = = > one shirt = 40 $ one trouser = 40 + 20 = 60 $ total trousers = 600 / 60 = 10 . e

<gadget id="calculator">20 + 20</gadget>
<output>40</output>
<gadget id="calculator">5 * 40</gadget>
<output>200</output>
<gadget id="calculator">800 - 200</gadget>
<output>600</output>
<gadget id="calculator">40 + 20</gadget>
<output>60</output>
<gadget id="calculator">600 / 60</gadget>
<output>10</output>
<result>10</result>


the average age of a class of 24 students is 23 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?

Explanation: "total age of all students = 24 ã — 23 total age of all students + age of the teacher = 25 ã — 24 age of the teacher = 25 ã — 24 â ˆ ’ 24 ã — 23 = 24 ( 25 â ˆ ’ 23 ) = 24 ã — 2 = 48 answer is c ."

subtract(multiply(add(24, 1), add(23, 1)), multiply(24, 23))

<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">23 + 1</gadget>
<output>24</output>
<gadget id="calculator">25 * 24</gadget>
<output>600</output>
<gadget id="calculator">24 * 23</gadget>
<output>552</output>
<gadget id="calculator">600 - 552</gadget>
<output>48</output>
<result>48</result>


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

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 45 : : 18 : x [ please pay attention , we have written 27 : 45 rather than 45 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 45 \ times 18 } { 27 } } x = 30 so 30 days will be required to get work done by 27 men . answer : c"

<gadget id="calculator">18 * 45</gadget>
<output>810</output>
<gadget id="calculator">810 / 27</gadget>
<output>30</output>
<result>30</result>


27 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?

Explanation: "( 27 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 60 60 – 27 = 33 answer : a"

subtract(divide(multiply(divide(multiply(27, 8), 30), 50), 6), 27)

<gadget id="calculator">27 * 8</gadget>
<output>216</output>
<gadget id="calculator">216 / 30</gadget>
<output>36/5 = around 7.2</output>
<gadget id="calculator">(36/5) * 50</gadget>
<output>360</output>
<gadget id="calculator">360 / 6</gadget>
<output>60</output>
<gadget id="calculator">60 - 27</gadget>
<output>33</output>
<result>33</result>


n and m are each 3 - digit integers . each of the numbers 2 , 3 , 4,5 , 6 , and 7 is a digit of either n or m . what is the smallest possible positive difference between n and m ?

Explanation: "you have 6 digits : 2 , 3 , 4 , 5 , 6 , 7 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 2 and 7 in the hundreds places and reserve them for the tens places . now what are the options ? try and make a pair with ( 3 * * and 4 * * ) . make the 3 * * number as large as possible and make the 4 * * number as small as possible . 376 and 425 ( difference is 49 ) or try and make a pair with ( 5 * * and 6 * * ) . make the 5 * * number as large as possible and make the 6 * * number as small as possible . we get 574 and 623 ( difference is 49 ) b"

subtract(subtract(const_100, multiply(subtract(7, 2), const_10)), const_1)

<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">50 - 1</gadget>
<output>49</output>
<result>49</result>


15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 4 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?

Explanation: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 4 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 4 * ( 2 / 3 ) ) days = > 45 days answer : e"

divide(multiply(multiply(15, 21), 8), multiply(multiply(21, 4), divide(2, 3)))

<gadget id="calculator">15 * 21</gadget>
<output>315</output>
<gadget id="calculator">315 * 8</gadget>
<output>2_520</output>
<gadget id="calculator">21 * 4</gadget>
<output>84</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">84 * (2/3)</gadget>
<output>56</output>
<gadget id="calculator">2_520 / 56</gadget>
<output>45</output>
<result>45</result>


on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor .

Explanation: "d = ( d - r ) / q = ( 21 - 1 ) / 10 = 20 / 10 = 2 b"

<gadget id="calculator">21 / 10</gadget>
<output>21/10 = around 2.1</output>
<gadget id="calculator">floor(21/10)</gadget>
<output>2</output>
<result>2</result>


if length of a rectangle is equal to side of a square and breadth of rectangle is half of length . if area of square is 36 sq . m . calculate the area of rectangle ?

Explanation: side of square = √ 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>


the price of a t . v . set worth rs . 70000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?

Explanation: "money paid in cash = rs . 1000 balance payment = ( 70000 - 1000 ) = rs . 69000 answer : c"

<gadget id="calculator">70_000 - 1_000</gadget>
<output>69_000</output>
<result>69_000</result>


the original price of a suit is $ 200 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?

Explanation: "0.8 * ( 1.2 * 200 ) = $ 192 the answer is a ."

subtract(add(200, divide(multiply(200, 20), const_100)), divide(multiply(add(200, divide(multiply(200, 20), const_100)), 20), const_100))

<gadget id="calculator">200 * 20</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 100</gadget>
<output>40</output>
<gadget id="calculator">200 + 40</gadget>
<output>240</output>
<gadget id="calculator">240 * 20</gadget>
<output>4_800</output>
<gadget id="calculator">4_800 / 100</gadget>
<output>48</output>
<gadget id="calculator">240 - 48</gadget>
<output>192</output>
<result>192</result>


in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ?

Explanation: let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e

divide(add(150, 30), add(add(const_2, const_1), const_1))

<gadget id="calculator">150 + 30</gadget>
<output>180</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">180 / 4</gadget>
<output>45</output>
<result>45</result>


on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?

Explanation: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d

<gadget id="calculator">2.8 + 2.8</gadget>
<output>5.6</output>
<gadget id="calculator">2.8 + 5.6</gadget>
<output>8.4</output>
<gadget id="calculator">8.4 + 5.6</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>


if the sample interest on a sum of money 10 % per annum for 2 years is $ 1200 , find the compound interest on the same sum for the same period at the same rate ?

Explanation: rate = 10 % time = 2 years s . i . = $ 1200 principal = 100 * 1200 / 10 * 2 = $ 6000 amount = 6000 ( 1 + 10 / 100 ) ^ 2 = $ 7260 c . i . = 7260 - 6000 = $ 1260 answer is a

subtract(add(divide(multiply(add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100)), 10), const_100), add(divide(multiply(1200, const_100), multiply(10, 2)), divide(multiply(divide(multiply(1200, const_100), multiply(10, 2)), 10), const_100))), divide(multiply(1200, const_100), multiply(10, 2)))

<gadget id="calculator">1_200 * 100</gadget>
<output>120_000</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">120_000 / 20</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 * 10</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 100</gadget>
<output>600</output>
<gadget id="calculator">6_000 + 600</gadget>
<output>6_600</output>
<gadget id="calculator">6_600 * 10</gadget>
<output>66_000</output>
<gadget id="calculator">66_000 / 100</gadget>
<output>660</output>
<gadget id="calculator">660 + 6_600</gadget>
<output>7_260</output>
<gadget id="calculator">7_260 - 6_000</gadget>
<output>1_260</output>
<result>1_260</result>


if 35 % of a number is 12 less than 50 % of that number , then the number is ?

Explanation: "let the number be x . then , 50 % of x - 35 % of x = 12 50 / 100 x - 35 / 100 x = 12 x = ( 12 * 100 ) / 15 = 80 . answer : d"

divide(12, divide(subtract(50, 35), const_100))

<gadget id="calculator">50 - 35</gadget>
<output>15</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">12 / (3/20)</gadget>
<output>80</output>
<result>80</result>


rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?

Explanation: let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 50000 + y so y = 30000 then x = 50000 - 30000 = 20000 first part = 20000 answer : a

divide(subtract(divide(multiply(50000, 20), const_100), 8000), divide(10, const_100))

<gadget id="calculator">50_000 * 20</gadget>
<output>1_000_000</output>
<gadget id="calculator">1_000_000 / 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 - 8_000</gadget>
<output>2_000</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">2_000 / (1/10)</gadget>
<output>20_000</output>
<result>20_000</result>


a number when divided by a certain divisor left remainder 245 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?

Explanation: "easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a"

<gadget id="calculator">245 * 2</gadget>
<output>490</output>
<gadget id="calculator">490 - 112</gadget>
<output>378</output>
<result>378</result>


85 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?

Explanation: "answer = a please refer diagram below 85 - 10 = 75"

<gadget id="calculator">85 - 10</gadget>
<output>75</output>
<result>75</result>


the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places

Explanation: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e"

divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(16, 14)), const_2)), const_2)

<gadget id="calculator">2 * (16 + 14)</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">2 * pi * (15/2)</gadget>
<output>15*pi = around 47.12389</output>
<gadget id="calculator">(15*pi) / 2</gadget>
<output>15*pi/2 = around 23.561945</output>
<result>15*pi/2 = around 23.561945</result>


a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be :

Explanation: "let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b"

<gadget id="calculator">17.5 / 40.25</gadget>
<output>0.434783</output>
<gadget id="calculator">28.75 * 0.434783</gadget>
<output>12.500011</output>
<result>12.500011</result>


x can do a piece of work in 4 hours ; y and z together can do it in 3 hours , while x and z together can do it in 2 hours . how long will y alone take to do it ?

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

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

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


in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 40 % of all the employees are men . what % of all the employee went to the picnic ?

Explanation: "total men in company 40 % means total women in company 60 % ( assume total people in company 100 % ) no of men employees attended picnic = 40 x ( 20 / 100 ) = 8 no of women employees attended picnic = 60 x ( 40 / 100 ) = 24 total percentage of employees attended the picnic = 8 + 24 = 32 % answer : a"

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

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(2/5) * (1/5)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * (2/5)</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">(2/25) + (6/25)</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>
<result>32</result>


excluding stoppages , the speed of a bus is 84 kmph and including stoppages , it is 70 kmph . for how many minutes does the bus stop per hour ?

Explanation: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( 14 / 84 x 60 ) min = 10 min answer : b"

multiply(const_60, divide(subtract(84, 70), 84))

<gadget id="calculator">84 - 70</gadget>
<output>14</output>
<gadget id="calculator">14 / 84</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">60 * (1/6)</gadget>
<output>10</output>
<result>10</result>


Explanation: 40 / 160 × 100 = 25 % answer : e

<gadget id="calculator">40 / 160</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty , how much money total will it cost to fuel all cars ?

Explanation: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 57 ) = 465.60 hence answer will be ( e )"

<gadget id="calculator">0.65 * 57</gadget>
<output>37.05</output>
<gadget id="calculator">37.05 * 12</gadget>
<output>444.6</output>
<result>444.6</result>


Explanation: answer : c ) 5940

multiply(multiply(multiply(multiply(const_2, const_2), multiply(multiply(const_3, const_3), const_3)), divide(divide(divide(135, const_3), const_3), const_3)), divide(22, const_2))

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">4 * 27</gadget>
<output>108</output>
<gadget id="calculator">135 / 3</gadget>
<output>45</output>
<gadget id="calculator">45 / 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">108 * 5</gadget>
<output>540</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">540 * 11</gadget>
<output>5_940</output>
<result>5_940</result>


the sale price sarees listed for rs . 280 after successive discount is 12 % and 8 % is ?

Explanation: "280 * ( 88 / 100 ) * ( 92 / 100 ) = 226 answer : b"

subtract(subtract(280, divide(multiply(280, 12), const_100)), divide(multiply(subtract(280, divide(multiply(280, 12), const_100)), 8), const_100))

<gadget id="calculator">280 * 12</gadget>
<output>3_360</output>
<gadget id="calculator">3_360 / 100</gadget>
<output>168/5 = around 33.6</output>
<gadget id="calculator">280 - (168/5)</gadget>
<output>1_232/5 = around 246.4</output>
<gadget id="calculator">(1_232/5) * 8</gadget>
<output>9_856/5 = around 1_971.2</output>
<gadget id="calculator">(9_856/5) / 100</gadget>
<output>2_464/125 = around 19.712</output>
<gadget id="calculator">(1_232/5) - (2_464/125)</gadget>
<output>28_336/125 = around 226.688</output>
<result>28_336/125 = around 226.688</result>


a girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction , takes 12 seconds to pass him . if the goods train is 1120 m long , find its speed .

Explanation: relative speed = ( 1120 / 12 ) m / s = ( 1120 / 12 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 40 = 296 kmph answer is b

subtract(divide(divide(1120, 12), const_0_2778), 40)

<gadget id="calculator">1_120 / 12</gadget>
<output>280/3 = around 93.333333</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(280/3) / (5/18)</gadget>
<output>336</output>
<gadget id="calculator">336 - 40</gadget>
<output>296</output>
<result>296</result>


a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?

Explanation: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b"

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))

<gadget id="calculator">1 * 1</gadget>
<output>1</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">5 + 21</gadget>
<output>26</output>
<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">(13/2) * 2</gadget>
<output>13</output>
<gadget id="calculator">13 - 4</gadget>
<output>9</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 66 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480

Explanation: "1 percent for 3 years = 66 1 percent for 1 year = 22 = > 100 percent = 2200 answer : c"

<gadget id="calculator">66 / 3</gadget>
<output>22</output>
<gadget id="calculator">22 * 100</gadget>
<output>2_200</output>
<result>2_200</result>


andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.82 . what is the median gasoline price ?

Explanation: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.82 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.82 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b

<gadget id="calculator">1.75 + 1.61</gadget>
<output>3.36</output>
<gadget id="calculator">3.36 + 1.79</gadget>
<output>5.15</output>
<gadget id="calculator">5.15 + 2.11</gadget>
<output>7.26</output>
<gadget id="calculator">7.26 + 1.96</gadget>
<output>9.22</output>
<gadget id="calculator">9.22 + 2.09</gadget>
<output>11.31</output>
<gadget id="calculator">11.31 + 1.82</gadget>
<output>13.13</output>
<gadget id="calculator">13.13 / 7</gadget>
<output>1.875714</output>
<gadget id="calculator">min(1.875714, 1.82)</gadget>
<output>1.82</output>
<result>1.82</result>


Explanation: "5 ^ x = 1 / 625 5 ^ x = 1 / 5 ^ 4 5 ^ x = 5 ^ - 4 x = - 4 b"

<gadget id="calculator">1 / 625</gadget>
<output>1/625 = around 0.0016</output>
<gadget id="calculator">log(1/625)</gadget>
<output>-log(625) = around -6.437752</output>
<gadget id="calculator">log(5)</gadget>
<output>log(5) = around 1.609438</output>
<gadget id="calculator">(-log(625)) / log(5)</gadget>
<output>-log(625)/log(5) = around -4</output>
<result>-log(625)/log(5) = around -4</result>


find the least number of complete years in which a sum of money put out at 45 % compound interest will be more than double of itself ?

Explanation: "2 years answer : a"

floor(add(divide(log(const_2), log(add(const_1, divide(45, const_100)))), const_1))

<gadget id="calculator">log(2)</gadget>
<output>log(2) = around 0.693147</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">1 + (9/20)</gadget>
<output>29/20 = around 1.45</output>
<gadget id="calculator">log(29/20)</gadget>
<output>log(29/20) = around 0.371564</output>
<gadget id="calculator">log(2) / log(29/20)</gadget>
<output>log(2)/log(29/20) = around 1.865488</output>
<gadget id="calculator">(log(2)/log(29/20)) + 1</gadget>
<output>1 + log(2)/log(29/20) = around 2.865488</output>
<gadget id="calculator">floor(1 + log(2)/log(29/20))</gadget>
<output>2</output>
<result>2</result>


the speed of the boat in still water in 12 kmph . it can travel downstream through 45 kms in 3 hrs . in what time would it cover the same distance upstream ?

Explanation: still water = 12 km / hr downstream = 45 / 3 = 15 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 15 / 2 = 9 km / hr so time taken in upstream = 45 / 9 = 5 hrs answer : d

divide(45, subtract(12, subtract(divide(45, 3), 12)))

<gadget id="calculator">45 / 3</gadget>
<output>15</output>
<gadget id="calculator">15 - 12</gadget>
<output>3</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">45 / 9</gadget>
<output>5</output>
<result>5</result>


the avg weight of a , b & c is 55 kg . if d joins the group , the avg weight of the group becomes 60 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 58 kg . what is the weight of a ?

Explanation: "a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 – 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d"

subtract(multiply(60, const_4), subtract(multiply(58, const_4), add(3, subtract(multiply(60, const_4), multiply(55, 3)))))

<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">58 * 4</gadget>
<output>232</output>
<gadget id="calculator">55 * 3</gadget>
<output>165</output>
<gadget id="calculator">240 - 165</gadget>
<output>75</output>
<gadget id="calculator">3 + 75</gadget>
<output>78</output>
<gadget id="calculator">232 - 78</gadget>
<output>154</output>
<gadget id="calculator">240 - 154</gadget>
<output>86</output>
<result>86</result>


if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ?

Explanation: explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a

add(subtract(3, const_2), divide(5, 10))

<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 105 liters of drink a to convert it to drink b ?

Explanation: "in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d ."

subtract(divide(multiply(multiply(divide(4, add(4, 3)), 105), 4), 3), multiply(divide(3, add(4, 3)), 105))

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">4 / 7</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">(4/7) * 105</gadget>
<output>60</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">240 / 3</gadget>
<output>80</output>
<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(3/7) * 105</gadget>
<output>45</output>
<gadget id="calculator">80 - 45</gadget>
<output>35</output>
<result>35</result>


at what rate percent per annum will a sum of money double in 9 years .

Explanation: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 9 ) ] % = 11.1 % per annum . answer : d"

<gadget id="calculator">100 / 9</gadget>
<output>100/9 = around 11.111111</output>
<result>100/9 = around 11.111111</result>


if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to :

Explanation: "explanation : 3 * 5 + 5 * 3 = ( 2 * 3 - 3 * 5 + 3 * 5 ) + ( 2 * 5 - 3 * 3 + 5 * 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer : a ) 22"

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">6 + 15</gadget>
<output>21</output>
<result>21</result>


noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 4 kilometers per hour ?

Explanation: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 4 = 2 * 3 * x / 3 + x x = 6 b is the answer"

divide(multiply(4, 3), subtract(multiply(const_2, 3), 4))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<result>6</result>


the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?

Explanation: x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.4 x ( 140 ) i . e . 140 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 140 = 71.43 i . e . y decreases from 100 to 71.43 i . e . decrease of 28.57 % c

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

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">100 / 140</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">1 - (5/7)</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 a and b are the roots of the equation x 2 - 6 x + 6 = 0 , then the value of a 2 + b 2 is :

Explanation: "sol . ( b ) the sum of roots = a + b = 6 product of roots = ab = 6 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 36 - 12 = 24 answer b"

add(power(divide(subtract(6, sqrt(subtract(power(6, 2), multiply(const_4, 6)))), 2), 2), power(divide(add(6, sqrt(subtract(power(6, 2), multiply(const_4, 6)))), 2), 2))

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<gadget id="calculator">12 ** (1/2)</gadget>
<output>2*sqrt(3) = around 3.464102</output>
<gadget id="calculator">6 - (2*sqrt(3))</gadget>
<output>6 - 2*sqrt(3) = around 2.535898</output>
<gadget id="calculator">(6 - 2*sqrt(3)) / 2</gadget>
<output>3 - sqrt(3) = around 1.267949</output>
<gadget id="calculator">(3 - sqrt(3)) ** 2</gadget>
<output>(3 - sqrt(3))**2 = around 1.607695</output>
<gadget id="calculator">6 + (2*sqrt(3))</gadget>
<output>2*sqrt(3) + 6 = around 9.464102</output>
<gadget id="calculator">(2*sqrt(3) + 6) / 2</gadget>
<output>sqrt(3) + 3 = around 4.732051</output>
<gadget id="calculator">(sqrt(3) + 3) ** 2</gadget>
<output>(sqrt(3) + 3)**2 = around 22.392305</output>
<gadget id="calculator">((3 - sqrt(3))**2) + ((sqrt(3) + 3)**2)</gadget>
<output>(3 - sqrt(3))**2 + (sqrt(3) + 3)**2 = around 24</output>
<result>(3 - sqrt(3))**2 + (sqrt(3) + 3)**2 = around 24</result>


6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?

Explanation: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose x and y and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : d

divide(factorial(3), multiply(subtract(6, const_1), const_4))

<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">6 / 20</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>


having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?

Explanation: "explanation : let the average score of the first 18 innings be n 18 n + 94 = 19 ( n + 4 ) = > n = 18 so , average score after 19 th innings = x + 4 = 22 . answer : d"

<gadget id="calculator">19 * 4</gadget>
<output>76</output>
<gadget id="calculator">94 - 76</gadget>
<output>18</output>
<gadget id="calculator">18 + 4</gadget>
<output>22</output>
<result>22</result>


a train 150 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?

Explanation: d = 72 * 5 / 18 = 25 = 500 – 150 = 299 . answer : c

subtract(multiply(25, multiply(72, const_0_2778)), 150)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">25 * 20</gadget>
<output>500</output>
<gadget id="calculator">500 - 150</gadget>
<output>350</output>
<result>350</result>


the present worth of a certain bill due sometime hence is rs . 1296 and the true discount is rs . 72 . what is the banker ' s discount ?

Explanation: explanation : bg = ( td ) 2 / pw = 722 / 1296 = 72 × 72 / 1296 = 12 × 12 / 36 = 12 / 3 = rs . 4 bg = bd – td = > 4 = bd - 72 = > bd = 72 + 4 = rs . 76 answer : option a

add(72, divide(power(72, const_2), 1296))

<gadget id="calculator">72 ** 2</gadget>
<output>5_184</output>
<gadget id="calculator">5_184 / 1_296</gadget>
<output>4</output>
<gadget id="calculator">72 + 4</gadget>
<output>76</output>
<result>76</result>


the grade point average of the entire class is 88 . if the average of one third of the class is 94 , what is the average of the rest of the class ?

Explanation: "let x be the number of students in the class . let p be the average of the rest of the class . 88 x = ( 1 / 3 ) 94 x + ( 2 / 3 ) ( p ) x 264 = 94 + 2 p 2 p = 170 p = 85 . the answer is d ."

divide(subtract(multiply(88, const_4), 94), subtract(const_4, const_1))

<gadget id="calculator">88 * 4</gadget>
<output>352</output>
<gadget id="calculator">352 - 94</gadget>
<output>258</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">258 / 3</gadget>
<output>86</output>
<result>86</result>


a truck covers a distance of 376 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?

Explanation: "explanation : speed of the truck = distance / time = 376 / 8 = 47 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 47 + 18 ) = 65 kmph distance travelled by car = 376 + 14 = 390 km time taken by car = distance / speed = 390 / 65 = 6 hours . answer – a"

<gadget id="calculator">376 + 14</gadget>
<output>390</output>
<gadget id="calculator">376 / 8</gadget>
<output>47</output>
<gadget id="calculator">47 + 18</gadget>
<output>65</output>
<gadget id="calculator">390 / 65</gadget>
<output>6</output>
<result>6</result>


the ratio of the ages of maala and kala is 3 : 5 . the total of their ages is 3.2 decades . the proportion of their ages after 0.8 decades will be [ 1 decade = 10 years ]

Explanation: let , maala ’ s age = 3 a and kala ’ s age = 5 a then 3 a + 5 a = 32 a = 4 maala ’ s age = 12 years and kala ’ s age = 20 years proportion of their ages after 8 is = ( 12 + 8 ) : ( 20 + 8 ) = 20 : 28 = 5 : 7 answer : b

divide(add(multiply(divide(multiply(3.2, 10), add(3, 5)), 3), multiply(0.8, 10)), add(multiply(5, divide(multiply(3.2, 10), add(3, 5))), multiply(0.8, 10)))

<gadget id="calculator">3.2 * 10</gadget>
<output>32</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">32 / 8</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">0.8 * 10</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">20 / 28</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>


mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 18 miles , how many miles was mike ' s ride ?

Explanation: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 18 ) = $ 12 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 12 0.25 * x = 9.5 x = 38 miles the answer is c ."

<gadget id="calculator">2.5 + 5</gadget>
<output>7.5</output>
<gadget id="calculator">0.25 * 18</gadget>
<output>4.5</output>
<gadget id="calculator">7.5 + 4.5</gadget>
<output>12</output>
<gadget id="calculator">12 - 2.5</gadget>
<output>9.5</output>
<gadget id="calculator">9.5 / 0.25</gadget>
<output>38</output>
<result>38</result>


a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent .

Explanation: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 55 percent 165 min . answer : d

<gadget id="calculator">55 / 20</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">(11/4) * 60</gadget>
<output>165</output>
<result>165</result>


in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

Explanation: "p ( neither pen is defective ) = 8 / 11 * 7 / 10 = 28 / 55 the answer is a ."

multiply(divide(subtract(11, 3), 11), divide(subtract(subtract(11, 3), const_1), subtract(11, const_1)))

<gadget id="calculator">11 - 3</gadget>
<output>8</output>
<gadget id="calculator">8 / 11</gadget>
<output>8/11 = around 0.727273</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">11 - 1</gadget>
<output>10</output>
<gadget id="calculator">7 / 10</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(8/11) * (7/10)</gadget>
<output>28/55 = around 0.509091</output>
<result>28/55 = around 0.509091</result>


a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical box each of edge 20 cm that can be packed inside the box is :

Explanation: "explanation : number of blocks = ( 160 x 100 x 60 / 20 x 20 x 20 ) = 120 answer : d"

volume_rectangular_prism(divide(1.6, divide(20, const_100)), divide(1, divide(20, const_100)), divide(divide(60, const_100), divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1.6 / (1/5)</gadget>
<output>8</output>
<gadget id="calculator">1 / (1/5)</gadget>
<output>5</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) / (1/5)</gadget>
<output>3</output>
<gadget id="calculator">8 * 5 * 3</gadget>
<output>120</output>
<result>120</result>


bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?

Explanation: if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a

divide(const_1, add(divide(const_1, 60), divide(const_1, multiply(60, const_3))))

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">1 / 180</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(1/60) + (1/180)</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">1 / (1/45)</gadget>
<output>45</output>
<result>45</result>


a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was

Explanation: "let the son ' s present age be x years . then , ( 40 - x ) = x x = 20 . son ' s age 5 years back = ( 20 - 5 ) = 15 years answer : c"

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 - 5</gadget>
<output>15</output>
<result>15</result>


the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 30 x 13 ) and ( 30 x 14 ) . larger number = ( 30 x 14 ) = 420 . answer : option c"

<gadget id="calculator">30 * 14</gadget>
<output>420</output>
<result>420</result>


find compound interest on rs . 7500 at 4 % per year for 2 years , compounded annually .

Explanation: "amount = rs [ 7500 * ( 1 + ( 4 / 100 ) 2 ] = rs ( 7500 * ( 26 / 25 ) * ( 26 / 25 ) ) = rs . 8112 . therefore , compound interest = rs . ( 8112 - 7500 ) = rs . 612 . answer is e ."

subtract(add(add(7500, divide(multiply(7500, 4), const_100)), divide(multiply(add(7500, divide(multiply(7500, 4), const_100)), 4), const_100)), 7500)

<gadget id="calculator">7_500 * 4</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 100</gadget>
<output>300</output>
<gadget id="calculator">7_500 + 300</gadget>
<output>7_800</output>
<gadget id="calculator">7_800 * 4</gadget>
<output>31_200</output>
<gadget id="calculator">31_200 / 100</gadget>
<output>312</output>
<gadget id="calculator">7_800 + 312</gadget>
<output>8_112</output>
<gadget id="calculator">8_112 - 7_500</gadget>
<output>612</output>
<result>612</result>


in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 178 votes . find the total number of valid votes ?

Explanation: let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 178 = > 4 x / 10 = 178 = > 4 x = 1780 = > x = 445 . answer : a

divide(178, divide(subtract(70, subtract(const_100, 70)), const_100))

<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">70 - 30</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">178 / (2/5)</gadget>
<output>445</output>
<result>445</result>


6 computers , each working at the same constant rate , together can process a certain amount of data in 9 days . how many additional computers , each working at the same constant rate , will be needed to process the same amount of data in 6 days ?

Explanation: explanation : if six computers require 9 days to process the data , thats a total of 54 computer - days the product of 6 and 9 . if you change the number of computers or the number of days , 54 will have to remain the product , whether that means 54 days of one computer or one day with 54 computers . in 6 days , the number of computers is : 6 c = 54 c = 9 9 computers is 3 more than the 6 that it took to do the job in 9 days , so the correct choice is ( a ) .

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

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">6 * (1/6)</gadget>
<output>1</output>
<gadget id="calculator">1 / 9</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<gadget id="calculator">9 - 6</gadget>
<output>3</output>
<result>3</result>


the radius of a cylindrical vessel is 7 cm and height is 4 cm . find the whole surface of the cylinder ?

Explanation: "r = 7 h = 4 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 11 ) = 484 answer : a"

<gadget id="calculator">2 * pi * 7 * (7 + 4)</gadget>
<output>154*pi = around 483.805269</output>
<result>154*pi = around 483.805269</result>


mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?

Explanation: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.00 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.958 0.708 0.958 1.208 1.458 1.708 1.958 total = $ 8.00 so this must be the answer . b"

add(divide(subtract(8.00, multiply(divide(multiply(subtract(6, const_1), 6), const_2), 0.25)), 6), multiply(subtract(6, const_1), 0.25))

<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 6</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 * 0.25</gadget>
<output>3.75</output>
<gadget id="calculator">8 - 3.75</gadget>
<output>4.25</output>
<gadget id="calculator">4.25 / 6</gadget>
<output>0.708333</output>
<gadget id="calculator">5 * 0.25</gadget>
<output>1.25</output>
<gadget id="calculator">0.708333 + 1.25</gadget>
<output>1.958333</output>
<result>1.958333</result>


a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt

Explanation: "explanation : area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a ) 680 rs"

multiply(divide(80, const_100), subtract(multiply(110, 65), multiply(subtract(110, 5), subtract(65, 5))))

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>
<gadget id="calculator">110 - 5</gadget>
<output>105</output>
<gadget id="calculator">65 - 5</gadget>
<output>60</output>
<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>
<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>
<gadget id="calculator">(4/5) * 850</gadget>
<output>680</output>
<result>680</result>


in a dairy farm , 16 cows eat 16 bags of husk in 16 days . in how many days one cow will eat one bag of husk ?

Explanation: explanation : one bag of husk = 16 cows per day ⇒ 16 × 1 × 16 = 1 × 16 × x for one cow = 16 days answer : a

<gadget id="calculator">16 / 16</gadget>
<output>1</output>
<gadget id="calculator">1 * 16</gadget>
<output>16</output>
<result>16</result>


in 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each , how many pumps will raise 2030 tons of water in 12 days of 11 hrs each ?

Explanation: explanation : pumps work time 12 1218 99 x 2030 132 = > 1218 / ( 912 * 99 ) = 2020 / ( x × 132 ) = > x = 15 pumps answer : option b

divide(multiply(multiply(multiply(12, 11), 9), 2030), multiply(multiply(12, 11), 1218))

<gadget id="calculator">12 * 11</gadget>
<output>132</output>
<gadget id="calculator">132 * 9</gadget>
<output>1_188</output>
<gadget id="calculator">1_188 * 2_030</gadget>
<output>2_411_640</output>
<gadget id="calculator">132 * 1_218</gadget>
<output>160_776</output>
<gadget id="calculator">2_411_640 / 160_776</gadget>
<output>15</output>
<result>15</result>


Explanation: "25.25 / 2000 = 2525 / 200000 = 0.01616 answer : d"

<gadget id="calculator">32.32 / 2_000</gadget>
<output>0.01616</output>
<result>0.01616</result>


george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?

Explanation: let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 5 % of 200 = 10 for taxi fare , so he is left with 190 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 90 ( 190 - 100 ) no of oranges he can buy = 90 / 4 = > 22,5 so , george can buy 20 oranges . d

multiply(subtract(subtract(const_1, divide(5, const_100)), divide(25, 50)), 50)

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">25 / 50</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(19/20) - (1/2)</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(9/20) * 50</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>


if 4 spiders make 4 webs in 4 days , then 1 spider will make 1 web in how many days ?

Explanation: "explanation : let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 4 | | : : 4 : 1 webs 4 : 1 | = > 1 * 4 * x = 4 * 1 * 4 = > x = 4 answer : d"

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


in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 36 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?

Explanation: "girls = 900 , boys = 1100 passed = ( 36 % of 1100 ) + ( 32 % of 900 ) = 396 + 288 = 684 failed = 2000 - 684 = 1316 failed % = [ ( 1316 / 2000 ) x 100 ] % = 65.8 % . answer : b"

multiply(divide(subtract(subtract(multiply(const_2, multiply(const_100, const_10)), multiply(divide(36, const_100), subtract(multiply(const_2, multiply(const_100, const_10)), 900))), multiply(divide(32, const_100), 900)), multiply(const_2, multiply(const_100, const_10))), const_100)

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">2_000 - 900</gadget>
<output>1_100</output>
<gadget id="calculator">(9/25) * 1_100</gadget>
<output>396</output>
<gadget id="calculator">2_000 - 396</gadget>
<output>1_604</output>
<gadget id="calculator">32 / 100</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">(8/25) * 900</gadget>
<output>288</output>
<gadget id="calculator">1_604 - 288</gadget>
<output>1_316</output>
<gadget id="calculator">1_316 / 2_000</gadget>
<output>329/500 = around 0.658</output>
<gadget id="calculator">(329/500) * 100</gadget>
<output>329/5 = around 65.8</output>
<result>329/5 = around 65.8</result>


john left home and drove at the rate of 50 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?

Explanation: "the total distance d traveled by john is given by d = 50 * 2 + 3 * 55 = 265 miles . answer d"

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">3 * 55</gadget>
<output>165</output>
<gadget id="calculator">100 + 165</gadget>
<output>265</output>
<result>265</result>


a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced x density of water = ( 0.06 x 1000 ) kg = 60 kg . answer : option b"

multiply(multiply(multiply(3, 2), divide(1, const_100)), const_1000)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">6 * (1/100)</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 1_000</gadget>
<output>60</output>
<result>60</result>


anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ?

Explanation: 5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a

subtract(35, add(multiply(5, 3), multiply(3, 4)))

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">35 - 27</gadget>
<output>8</output>
<result>8</result>


if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c â ˆ ’ a ?

Explanation: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 160 - - 2 subtracting 1 from 2 we have c - a = 70 ; answer : b"

it can not be determined from the information given

subtract(multiply(80, const_2), multiply(45, const_2))

<gadget id="calculator">80 * 2</gadget>
<output>160</output>
<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">160 - 90</gadget>
<output>70</output>
<result>70</result>


a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?

Explanation: "800 * 8.2 6560.0 gm 6.56 kg answer : a"

<gadget id="calculator">8.2 * 800</gadget>
<output>6_560</output>
<gadget id="calculator">6_560 / 1_000</gadget>
<output>164/25 = around 6.56</output>
<result>164/25 = around 6.56</result>


if a 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 tails up on the first 4 flips and not on the last flip ?

Explanation: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b

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


the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 990 square meters , what is the depth of the channel ( in meters ) ?

Explanation: "1 / 2 * d * ( 14 + 8 ) = 990 d = 90 the answer is e ."

divide(990, divide(add(14, 8), const_2))

<gadget id="calculator">14 + 8</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">990 / 11</gadget>
<output>90</output>
<result>90</result>


income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 14000 , then find his savings ?

Explanation: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 14000 = > x = 2800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 2800 . answer : b"

subtract(14000, multiply(divide(4, 5), 14000))

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 14_000</gadget>
<output>11_200</output>
<gadget id="calculator">14_000 - 11_200</gadget>
<output>2_800</output>
<result>2_800</result>


two employees x and y are paid a total of rs . 750 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 750 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 750 ⇒ y [ 12 / 10 + 1 ] = 750 ⇒ 22 y / 10 = 750 ⇒ 22 y = 7500 ⇒ y = 7500 / 22 = rs . 340.90 e )"

divide(multiply(750, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">750 * 10</gadget>
<output>7_500</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">7_500 / 22</gadget>
<output>3_750/11 = around 340.909091</output>
<result>3_750/11 = around 340.909091</result>


the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 19 . find the sum :

Explanation: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 19 , the sum = 400 × 19 = 7600 answer b"

divide(19, subtract(power(add(const_1, divide(5, const_100)), 2), add(const_1, multiply(2, divide(5, const_100)))))

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">2 * (1/20)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(441/400) - (11/10)</gadget>
<output>1/400 = around 0.0025</output>
<gadget id="calculator">19 / (1/400)</gadget>
<output>7_600</output>
<result>7_600</result>


machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 60 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?

Explanation: "machine b produces 100 part in 60 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 60 / 2 = 30 minutes . now , machine a produces 100 parts in 30 minutes which is 100 / 30 = 10 / 3 parts / minute . 10 / 3 parts x a total of 6 minutes = 20 a"

multiply(multiply(divide(100, 60), const_2), 6)

<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) * 2</gadget>
<output>10/3 = around 3.333333</output>
<gadget id="calculator">(10/3) * 6</gadget>
<output>20</output>
<result>20</result>


if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 12 ?

Explanation: there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : b .

subtract(power(add(5, const_2), 2), multiply(12, const_4))

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">49 - 48</gadget>
<output>1</output>
<result>1</result>


set j consists of 5 consecutive even numbers . if the smallest term in the set is - 2 , what is the range of the positive integers in set j ?

Explanation: since there are only 5 integers , another approach is the just list all 5 . we get : - 2 , 0,2 , 4 , 6 range of positive integers = 6 - 2 = 4 answer : c

subtract(add(negate(2), multiply(subtract(5, const_1), 2)), 2)

<gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">(-2) + 8</gadget>
<output>6</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<result>4</result>


the sum of all the integers g such that - 26 < g < 24 is

Explanation: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 g = - 49 . d is the answer ."

add(add(negate(26), const_1), add(add(negate(26), const_1), const_1))

<gadget id="calculator">-26</gadget>
<output>-26</output>
<gadget id="calculator">(-26) + 1</gadget>
<output>-25</output>
<gadget id="calculator">(-25) + 1</gadget>
<output>-24</output>
<gadget id="calculator">(-25) + (-24)</gadget>
<output>-49</output>
<result>-49</result>


a student chose a number , multiplied it by 2 , then subtracted 180 from the result and got 104 . what was the number he chose ?

Explanation: "solution : let x be the number he chose , then 2 * x * 180 = 104 2 x = 284 x = 142 correct answer d"

<gadget id="calculator">104 + 180</gadget>
<output>284</output>
<gadget id="calculator">284 / 2</gadget>
<output>142</output>
<result>142</result>


two brothers take the same route to school on their bicycles , one gets to school in 25 minutes and the second one gets to school in 36 minutes . the ratio of their speeds is

Explanation: solution let us name the brothers as a and b . = ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 36 = 5 : 6 answer d

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<result>5/6 = around 0.833333</result>


the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 9 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 9 = 45 km imo , correct answer is ` ` c . ' '"

multiply(60, divide(multiply(5, 9), 60))

<gadget id="calculator">5 * 9</gadget>
<output>45</output>
<gadget id="calculator">45 / 60</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">60 * (3/4)</gadget>
<output>45</output>
<result>45</result>


in a certain warehouse , 50 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?

Explanation: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 50 % of the packages weigh less than 75 pounds so , 50 % oft = number of packages that weigh less than 75 pounds 50 % of 240 = 120 , so 120 packages weigh less than 75 pounds of those 120 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 120 - 48 = 72 = c"

subtract(divide(multiply(multiply(divide(48, subtract(const_100, 80)), const_100), 50), const_100), 48)

<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">48 / 20</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 100</gadget>
<output>240</output>
<gadget id="calculator">240 * 50</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<gadget id="calculator">120 - 48</gadget>
<output>72</output>
<result>72</result>


in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :

Explanation: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph . = 8 kmph . answer c"

<gadget id="calculator">11 + 5</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


the ratio of the cost price and the selling price is 4 : 5 . the profit percent is ?

Explanation: "let c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % . answer : c"

multiply(subtract(divide(5, 4), const_1), const_100)

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) - 1</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


if 45 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 65 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .

Explanation: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 100 + 0.50 x 78 + 0.05 x 63 = 87.15 the class average ( rounded ) is 87 % final answer b ) 87 %"

divide(add(add(multiply(45, 100), multiply(50, 78)), multiply(subtract(const_100, add(45, 50)), 65)), const_100)

<gadget id="calculator">45 * 100</gadget>
<output>4_500</output>
<gadget id="calculator">50 * 78</gadget>
<output>3_900</output>
<gadget id="calculator">4_500 + 3_900</gadget>
<output>8_400</output>
<gadget id="calculator">45 + 50</gadget>
<output>95</output>
<gadget id="calculator">100 - 95</gadget>
<output>5</output>
<gadget id="calculator">5 * 65</gadget>
<output>325</output>
<gadget id="calculator">8_400 + 325</gadget>
<output>8_725</output>
<gadget id="calculator">8_725 / 100</gadget>
<output>349/4 = around 87.25</output>
<result>349/4 = around 87.25</result>


of the votes cast on a certain proposal , 62 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )

Explanation: let x be the total number of votes cast . 0.6 x = 0.4 x + 62 0.2 x = 62 x = 310 the answer is d .

divide(62, subtract(subtract(const_1, divide(40, const_100)), divide(40, const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) - (2/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">62 / (1/5)</gadget>
<output>310</output>
<result>310</result>


how many of the integers between 20 and 80 are even ?

Explanation: "number start between 20 to 80 is 60 numbers half of them is even . . which is 30 answer : b"

<gadget id="calculator">80 - 20</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>30</result>


if a and b are positive integers , and a = 5 b + 20 , the greatest common divisor of a and b can not be

Explanation: if b is 2 , 4 , 5 , or 10 , then gcd of a and b is 2 , 4 , 5 , and 10 respectively . so , by poe the answer must be d . still : if b is a multiple of 6 , then a is 20 greater than a multiple of 6 , so not a multiple of 6 , so both of them can not be divisive by 6 . answer : d .

<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<result>6</result>


Explanation: "35 * 18 / 5 = 126 kmph answer : c"

<gadget id="calculator">35 / 1_000</gadget>
<output>7/200 = around 0.035</output>
<gadget id="calculator">(7/200) * 3_600</gadget>
<output>126</output>
<result>126</result>


the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?

Explanation: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.5 = 1665 answer : d"

multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, 1)), 2.50), 3)

<gadget id="calculator">3_136 ** (1/2)</gadget>
<output>56</output>
<gadget id="calculator">56 * 4</gadget>
<output>224</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">224 - 2</gadget>
<output>222</output>
<gadget id="calculator">222 * 2.5</gadget>
<output>555</output>
<gadget id="calculator">555 * 3</gadget>
<output>1_665</output>
<result>1_665</result>


there are 690 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?

Explanation: female = x male = 690 - x x / 2 + 690 - x / 4 = 1 / 3 * ( 690 ) = 230 x = 230 x / 2 = 115 is supposed to be the answer m is missing something correct option c

divide(subtract(multiply(divide(690, const_3), const_4), 690), const_2)

<gadget id="calculator">690 / 3</gadget>
<output>230</output>
<gadget id="calculator">230 * 4</gadget>
<output>920</output>
<gadget id="calculator">920 - 690</gadget>
<output>230</output>
<gadget id="calculator">230 / 2</gadget>
<output>115</output>
<result>115</result>


find the area of a parallelogram with base 20 cm and height 40 cm ?

Explanation: "area of a parallelogram = base * height = 20 * 40 = 800 cm 2 answer : c"

<gadget id="calculator">20 * 40</gadget>
<output>800</output>
<result>800</result>


a can do a piece of work in 6 hours ; b and c together can do it in 4 hours , which a and c together can do it in 3 hours . how long will b alone take to do it ?

Explanation: "a ' s 1 hour work = 1 / 6 ; ( b + c ) ' s 1 hour work = 1 / 4 ; ( a + c ) ' s 1 hour work = 1 / 3 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 6 ) = 5 / 12 b ' s 1 hour work = ( 5 / 12 - 1 / 3 ) = 1 / 12 b alone will take 12 hours to do the work . answer : d"

divide(const_1, subtract(divide(const_1, 4), subtract(divide(const_1, 3), divide(const_1, 6))))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/3) - (1/6)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/4) - (1/6)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


a train 250 m long running at 72 kmph crosses a platform in 30 sec . what is the length of the platform ?

Explanation: "d = 72 * 5 / 18 = 30 = 600 â € “ 250 = 350 m answer : a"

subtract(multiply(30, multiply(72, const_0_2778)), 250)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">30 * 20</gadget>
<output>600</output>
<gadget id="calculator">600 - 250</gadget>
<output>350</output>
<result>350</result>


4 shepherds were watching over the flocks and they were commenting on how many sheep they each had . if ram had 3 more sheep than he would have one less than rahul . wheras akar has the same number as the other 3 shepherds put togeher . if john had 3 less sheep he would have exactly trile the number of ram . if they were evenly distributed if they would each have 11 seep how many sheep did ram have ?

Explanation: akar has = ram + rahul + john after evenly distribution each has 11 . so , total no . is 44 so , akar has = 22 & ram + rahul + john = 22 also ram = rahul - 4 & john - 3 = 3 * ram solving these we get the sol . answer : b

divide(subtract(multiply(11, const_2), add(4, 3)), add(4, const_1))

<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">22 - 7</gadget>
<output>15</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<result>3</result>