euclaise/mathqa_programs huggingface dataset:
Problem: a certain bag contains 60 balls — 22 white , 10 green , 7 yellow , 15 red , and 6 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.65 , c ) 0.54 , d ) 0.85 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 10 + 17 ) / 60 = 39 / 60 = 0.65 . answer : b ."
Answer: b
Python program:
a = 22 + 10 
b = a + 7 
c = b / 60
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 5 cm , and bd = 9 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: "putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 11 ( bd = 9 ) cd is 11 - 5 = 6 . ans d"
Answer: d
Python program:
a = 5 - 2
Problem: if the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 8 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 2 , d ) 16 , e ) 18
Rationale: "let length of rectangle = l 4 ^ 2 = l * 8 = > l = 16 / 8 = 2 answer c"
Answer: c
Python program:
a = 4 ** 2
b = a / 8
Problem: the average of 6 numbers is 6.8 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 9.2 . what number is multiplied by 3 ?
Options: a ) 9.5 , b ) 8.0 , c ) 7.2 , d ) 5.0 , e ) 4.0
Rationale: "the average of 6 numbers is 6.8 the sum of 6 numbers will be 6.8 x 6 = 40.8 the average of 6 number after one of the number is multiplied by 3 is 9.2 the sum of the numbers will now be 9.2 x 6 = 55.2 so the sum has increased by 55.2 - 40.8 = 14.4 let the number multiplied by 3 be n then , 3 n = n + 14.4 or 2 n = 14.4 or n = 7.2 answer : - c"
Answer: c
Python program:
a = 9 * 2
b = 6 * 8
c = a - b
Problem: two trains 200 m and 800 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 10.9 , c ) 36 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 200 + 800 = 1000 m . required time = 1000 * 9 / 250 = 36 sec . answer : c"
Answer: c
Python program:
a = 200 + 800 
b = 60 + 40 
c = b * const_0_2778
d = a / c
Problem: if 3 < x < 6 < y < 7 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 7 ; 3 < x y < 7 3 + y < x + 7 y - x < 4 . positive integer difference is 3 ( for example y = 6.5 and x = 3.5 ) answer : a ."
Answer: a
Python program:
a = 7 - 3
b = a - 1
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 96 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 96 2 l ^ 2 / 3 = 96 l ^ 2 = 144 l = 12 cm the answer is b ."
Answer: b
Python program:
a = 96 / 10
Problem: in a group of 90 people , 55 have visited iceland and 33 have visited norway . if 51 people have visited both iceland and norway , how many people have visited neither country ?
Options: a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54
Rationale: "this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 90 = 55 + 33 - 51 + ( # in neither group ) = 53 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d"
Answer: d
Python program:
a = 55 + 33 
b = a - 51
c = 90 - b
Problem: a small company reduced its faculty by approximately 14 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 227 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 14 % reduction in employees number is . 86 x but we are given . 86 x = 195 x = 227 so the original number of employees is 227 correct answer - b"
Answer: b
Python program:
a = 100 - 14
b = a / 100
c = 195 / b
Problem: in a dairy farm , 40 cows eat 40 bags of husk in 40 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 1 / 40 , c ) 40 , d ) 80 , e ) 1 / 80
Rationale: "assume that in x days , one cow will eat one bag of husk . more cows , less days ( indirect proportion ) more bags , more days ( direct proportion ) hence we can write as cowsbags 40 : 11 : 40 ⎫ ⎭ ⎬ : : x : 40 ⇒ 40 × 1 × 40 = 1 × 40 × x ⇒ x = 40 answer : c"
Answer: c
Python program:
a = 40 / 40
b = a * 40
Problem: the average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 99 , d ) 26 , e ) 27
Rationale: total age increased = ( 8 * 2 ) years = 8 years . sum of ages of two new men = ( 21 + 23 + 8 ) years = 52 years average age of two new men = ( 52 / 2 ) years = 26 years . answer : d
Answer: d
Python program:
a = 21 + 23 
b = a / 2
c = 1 * 4
d = b + c
Problem: one type of liquid contains 25 % of kerosene , the other contains 30 % of kerosene . p can is filled with 6 parts of the first liquid and 4 parts of the second liquid . find the percentage of the kerosene in the new mixture .
Options: a ) 28 % , b ) 25 % , c ) 30 % , d ) 27 % , e ) 35 %
Rationale: let p be filled by 60 lts of 1 st liquid and 40 lts . of 2 nd liquid . amount of kerosene = ( 25 * 60 / 100 ) + ( 30 * 40 / 100 ) = 27 lts . % of kerosene = 27 % answer : d
Answer: d
Python program:
a = 25 / 100
b = 6 * a
c = 30 / 100
d = 4 * c
e = b + d 
f = 6 + 4 
g = e * f
Problem: the ratio of income of anand to that of balu is 5 : 4 and the expenditure of anand to that of balu is 3 : 2 . if at the end of the year , each saves rs , 800 , the income of anand is :
Options: a ) rs 1600 , b ) rs 1800 , c ) rs 2000 , d ) rs 2200 , e ) none of these
Rationale: explanation : let the income of anand and balu be 5 x and 4 x and . the expenditures of anand and balu be 3 y and 2 y . then , 5 x 3 y = 800 and 4 x 2 y = 800 . on solving we get : x = 400 . as income = 5 x = rs . 2000 . answer : c
Answer: c
Python program:
a = 800 * 5
b = 800 * 4
c = a - b
d = 3 * 4
e = 2 * 5
f = d - e
g = c / f
h = g * 3
i = 800 + h
Problem: the largest natural number by which the product of 3 consecutive even natural numbers is always divisible , is
Options: a ) 16 , b ) 24 , c ) 48 , d ) 96 , e ) 78
Rationale: solution required number = ( 2 × 4 × 6 ) = 48 . answer c
Answer: c
Python program:
a = 3 - 1
b = 3 - 1
c = 3 - 1
d = b * c
e = a * d
f = 3 - 1
g = 3 - 1
h = f * g
i = 3 - 1
j = h + i 
k = e * j
Problem: a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 482 more if the interest were payable half - yearly , then it were pay able yearly . find the sum ?
Options: a ) 2099 , b ) 6086 , c ) 2976 , d ) 2000 , e ) 3862
Rationale: "p ( 11 / 10 ) 4 - p ( 6 / 5 ) 2 = 482 p = 2000 answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 + 1 
e = c + d
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 5 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 15
Rationale: "on the way down , the rate is 1.5 * 5 = 7.5 miles per day . the distance of the route down the mountain is 2 * 7.5 = 15 miles . the answer is e ."
Answer: e
Python program:
a = 5 * 2
b = 3 / 2
c = a * b
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 4 intersects line l at ( p , 5 ) and ( t , - 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) 2 , c ) - 4 , d ) - 6 , e ) - 10
Rationale: "we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , 5 ) . hence , x = p and y = 5 should sactisfy the graph . soliving 5 = - p 2 + 4 p 2 = 1 p = + or - 1 simillarly point ( t , - 7 ) should satisfy the equation . hence x = t and y = - 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 7 - 5 ) / ( 4 - 1 ) = - 4 imo option c is correct answer ."
Answer: c
Python program:
a = 7 - 5
b = 4 + 7 
c = math.sqrt(b)
d = 5 + 4 
e = math.sqrt(d)
f = c - e
g = a / f
Problem: the value of a machine depreciates at 25 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
Options: a ) $ 258375 , b ) $ 438375 , c ) $ 128375 , d ) $ 108375 , e ) $ 158375
Rationale: "the value of the machine after two years = 0.75 * 0.75 * 1 , 50,000 = $ 84,375 sp such that a profit of $ 24,000 is made = 84,375 + 24,000 = $ 1 , 08,375 d"
Answer: d
Python program:
a = 25 / 100
b = 1 - a
c = 25 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 25 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: triangle atriangle b are similar triangles with areas 2268 units square and 2527 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10 , b ) 18 : 19 , c ) 23 : 27 , d ) 13 : 17 , e ) 15 : 23
Rationale: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2268 / 2527 ( x ^ 2 / y ^ 2 ) = ( 18 * 18 * 7 ) / ( 19 * 19 * 7 ) ( x ^ 2 / y ^ 2 ) = 18 ^ 2 / 19 ^ 2 x / y = 18 / 19 ans = b"
Answer: b
Python program:
a = 2268 / 2527
b = math.sqrt(a)
Problem: 40 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ?
Options: a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 170 litres , e ) none of these
Rationale: "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 40 = 53.33 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 53.33 = 80 litres . answer a"
Answer: a
Python program:
a = 800 * 600
b = 40 / a
c = 800 * b
d = 1200 * c
Problem: a and b go around a circular track of length 600 m on a cycle at speeds of 24 kmph and 60 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 176 sec , c ) 178 sec , d ) 180 sec , e ) 189 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 600 / ( 24 * 5 / 18 ) , 600 / ( 60 * 5 / 18 ) } = 180 sec . answer : d"
Answer: d
Python program:
a = 60 * const_0_2778
b = 24 * const_0_2778
c = a - b
d = 600 / c
Problem: the captain of a cricket team of 11 members is 28 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 25 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 28 + 31 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 50 2 x = 50 x = 25 so , average age of the team is 25 years . answer e"
Answer: e
Python program:
a = 28 + 3 
b = 28 + a 
c = 3 * 3
d = b - c
e = d / 2
Problem: during 2003 , a company produced an average of 2,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 150 % over its 2003 average ?
Options: a ) 287,000 , b ) 290,000 , c ) 284,000 , d ) 285,000 , e ) 286,000
Rationale: company produced 12 * 2000 = 24,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 24,000 . the gives the average of ( x + 24,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 36,000 + 150 % ( 36,000 ) = 80,000 . so : ( x + 36,000 ) / 4 = 80,000 x + 36,000 = 320,000 x = 284,000 the answer is c .
Answer: c
Python program:
a = 2007 - 2003
b = a / 2
c = 150 * b
Problem: a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 30 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 30 ) = 285 option b"
Answer: b
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: a train speeds past a pole in 15 sec and a platform 150 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 225 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 150 ) / 25 = x / 15 = > x = 225 m . answer : option d"
Answer: d
Python program:
a = 2 - 1
b = 150 * a
Problem: there are 2 sections a and b in a class , consisting of 40 and 30 students respectively . if the average weight of section a is 50 kg and that of section b is 60 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 69.15 kg , e ) 54.28 kg
Rationale: "total weight of 40 + 30 students = 40 * 50 + 30 * 60 = 2000 + 1800 average weight of the class is = 3800 / 70 = 54.28 kg answer is e"
Answer: e
Python program:
a = 40 * 50
b = 30 * 60
c = a + b 
d = 40 + 30 
e = c / d
Problem: a customer purchased a package of ground beef at a cost of $ 1.76 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 36 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.00 , b ) $ 2.25 , c ) $ 2.50 , d ) $ 2.75 , e ) $ 3.00
Rationale: "for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.76 . let x be the price per pound for the steak . then 0.64 x = 176 x = 176 / 0.64 = $ 2.75 the answer is d ."
Answer: d
Python program:
a = const_0_25 * 2
b = const_0_33 * 1
c = a + b 
d = 1 / 76
Problem: a train 275 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 5 sec , c ) 15 sec , d ) 6 sec , e ) 12 sec
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 275 * 3 / 55 ] sec = 15 sec answer : c"
Answer: c
Python program:
a = 275 / 1000
b = 60 + 6 
c = a / b
d = 3600 * c
Problem: lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 74,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.14544 , c ) 0.25632 , d ) 0.2139 , e ) 0.63435
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 374000 x \ therefore required percentage = \ inline \ frac { 800 x } { 374000 } \ times 100 = 0.21390 d"
Answer: d
Python program:
a = 60 / 100
b = 480 / a
c = 3 * 100
d = c * 1000
e = 4 * 10
f = e + 4 
g = f * 1000
h = d + g 
i = b / h
j = i * 100
Problem: the average ( arithmetic mean ) of the even integers from 16 to 44 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 14 to 56 inclusive ?
Options: a ) 10 , b ) 5 , c ) 15 , d ) 20 , e ) 7
Rationale: "so , according to a mean of a set of even numbers from 16 to 44 = ( 16 + 44 ) / 2 = 30 and mean of a set of even numbers from 14 to 56 = ( 14 + 56 ) / 2 = 35 difference = 35 - 30 = 5 answer : b ."
Answer: b
Python program:
a = 56 + 14 
b = a / 2
c = 44 + 16 
d = c / 2
e = b - d
Problem: if a card is drawn from a well shuffled pack of cards , the probability of drawing a spade or a king is ?
Options: a ) 4 / 15 , b ) 4 / 10 , c ) 4 / 18 , d ) 4 / 13 , e ) 4 / 11
Rationale: "p ( s ᴜ k ) = p ( s ) + p ( k ) - p ( s ∩ k ) , where s denotes spade and k denotes king . p ( s ᴜ k ) = 13 / 52 + 4 / 52 - 1 / 52 = 4 / 13 answer : d"
Answer: d
Python program:
a = 3 / const_52
b = const_52 / 4
c = b / const_52
d = a + c
Problem: two employees a and b are paid a total of rs . 570 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 228 , e ) s . 282
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 570 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 570 ⇒ y [ 15 / 10 + 1 ] = 570 ⇒ 25 y / 10 = 570 ⇒ 25 y = 5700 ⇒ y = 5700 / 25 = rs . 228 d )"
Answer: d
Python program:
a = 150 / 100
b = a + 1 
c = 570 / b
Problem: a company has two models of computers , model m and model n . operating at a constant rate , a model m computer can complete a certain task in 36 minutes and a model n computer can complete the same task in 18 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model m computers were used ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: "let ' s say 1 work is processing 36 gb of data . model m : 1 gb per min model n : 2 gb per min working together , 1 m and 1 n = 3 gb per min so , 12 times as many computers would work at 36 gb per min . so no . of m = 12 answer is a"
Answer: a
Python program:
a = 1/(18)
b = 1/(36)
c = a + b 
d = 1/(c)
Problem: a retailer sold an appliance for $ 70 . if the retailer ' s gross profit on the appliance was 25 percent of the retailer ' s cost for the appliance , how many dollars was the retailer ' s gross profit ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 20 , d ) $ 24 , e ) $ 25
Rationale: "gross profit = selling price - cost = 70 - x 70 - x = 1 / 4 x x = 56 gp = 70 - 56 = 14"
Answer: a
Python program:
a = 25 / 70
b = a + 1 
c = 1 / b
d = c * 70
e = 70 - d
Problem: a sporting goods store sold 60 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 200 , what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 20 , d ) 4 , e ) 2
Rationale: the wording of the question is slightly misleading . when a question asks what is thefewestthatcouldhave been sold , it is suggesting that there could be many different quantities sold . in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 60 3 x + 4 y = 200 x = 60 - y 3 ( 60 - y ) + 4 y = 200 180 - 3 y + 4 y = 200 y = 20 answer : c
Answer: c
Python program:
a = 60 * 3
b = 200 - a
Problem: there are 16 bees in the hive , then 7 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 23 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 7 = 23 . answer is b .
Answer: b
Python program:
a = 16 + 7
Problem: laura took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 6 % interest = ( 6 / 100 ) * 35 = 2.10 $ total amount that laura owes a year later = 35 + 2.1 = 37.1 $ answer b"
Answer: b
Python program:
a = 6 / 100
b = a * 35
c = b + 35
Problem: with both inlets open , a water tank will be filled with water in 24 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 2,000 , b ) 10,500 , c ) 11,750 , d ) 12,000 , e ) 13,000
Rationale: the work done by inlet a and b together in 1 min = 1 / 24 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 24 ) - ( 1 / 120 ) = 1 / 30 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 30 ) - ( 1 / 120 ) = 50 cubic meter i . e . tank = 40 * 50 = 2000 cubic meter answer : option a
Answer: a
Python program:
a = const_60 / 24
b = 1/(2)
c = a - b
d = c / const_60
e = const_60 * 2
f = 1/(e)
g = d - f
h = 50 / g
i = h / 1000
Problem: if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 36 m long cloth in ?
Options: a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 6 = 1 day . option ' a '"
Answer: a
Python program:
a = 4 * 2
b = 48 / a
c = b * 6
d = 36 / c
Problem: find the area of a rhombus one side of which measures 20 cm and one diagonal is 23 cm .
Options: a ) 100 cm 2 , b ) 150 cm 2 , c ) 300 cm 2 , d ) 368 cm 2 , e ) 400 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 23 x 32 ) cm 2 = 368 cm 2 answer : option d"
Answer: d
Python program:
a = 1 / 2
b = a * 23
c = 20 * 20
d = c * 4
e = 23 * 23
f = d - e
g = math.sqrt(f)
h = b * g
i = h + 23
Problem: compound interest of rs . 6000 at 10 % per annum for 1 1 / 2 years will be ( interest compounded half yearly ) .
Options: a ) rs . 473 , b ) rs . 374 , c ) rs . 495 , d ) rs . 945 , e ) none of the above
Rationale: "10 % interest per annum will be 5 % interest half yearly for 3 terms ( 1 1 / 2 years ) so compound interest = 6000 [ 1 + ( 5 / 100 ) ] ^ 3 - 6000 = 6000 [ ( 21 / 20 ) ^ 3 - 1 ] = 6000 ( 9261 - 8000 ) / 8000 = 6 * 1261 / 8 = 945 answer : d"
Answer: d
Python program:
a = 10 / 2
b = a / 100
c = 1 + b 
d = 1 / 2
e = 1 + d 
f = e * 2
g = c ** f
h = 6000 * g
i = h - 6000
Problem: a and b started a business investing rs . 75,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 4 , e ) 13 : 4
Rationale: "a : b = 75000 : 20000 = 75 : 20 = 13 : 4 answer : e"
Answer: e
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h