euclaise/mathqa_programs huggingface dataset:
Problem: find the simple interest on rs . 450 for 8 months at 5 paisa per month ?
Options: a ) 277 , b ) 270 , c ) 180 , d ) 266 , e ) 121
Rationale: "i = ( 450 * 8 * 5 ) / 100 = 180 answer : c"
Answer: c
Python program:
a = 8 / 100
b = 450 * a
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 49 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 28
Rationale: "12 * 49 = 588 588 % 21 = 28 answer : e"
Answer: e
Python program:
a = 12 * 49
b = a / 21
Problem: 54671 - 18456 - 33466 = ?
Options: a ) 2749 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 6468
Rationale: "a if we calculate we will get 2749"
Answer: a
Python program:
a = 54671 / 100
b = a * 18456
c = 1 / 3
d = 54671 / 100
e = d * 18456
f = c * e
g = b - f
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 52 %
Rationale: "let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : e"
Answer: e
Python program:
a = 4 * 6
b = 6 * 4
c = a + b 
d = 100 - c
Problem: the effective annual rate of interest corresponding to a nominal rate of 12 % per annum payable half - yearly is ?
Options: a ) 16.06 % , b ) 16.07 % , c ) 12.36 % , d ) 6.09 % , e ) 6.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 6 / 100 ) 2 ] = rs . 112.36 effective rate = ( 112.36 - 100 ) = 12.36 % answer : c"
Answer: c
Python program:
a = 12 / 2
b = 12 / 2
c = a + b 
d = 12 / 2
e = 12 / 2
f = d * e
g = f / 100
h = c + g
Problem: an association of mathematics teachers has 1600 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 14.5 % , e ) 19.6 %
Rationale: total umber of members = 1600 number of members that cast votes = 525 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 525 = 315 percent of total membership that voted for winning candidate = ( 315 / 1600 ) * 100 = 19.6 % answer e
Answer: e
Python program:
a = 525 * 60
b = a / 100
c = b * 100
d = c / 1600
Problem: if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 13 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 13 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 13 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 13 is 12 . answer : d ."
Answer: d
Python program:
a = 3 + 2 
b = a ** 2
c = 13 * 4
d = b - c
Problem: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.25 , b ) $ 3.00 , c ) $ 3.25 , d ) $ 3.65 , e ) $ 4.80
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 60 4 x / 15 = 60 x = 225 = $ 2.25 the answer is a ."
Answer: a
Python program:
a = 3 / 5
b = 1 / 3
c = 3 / 5
d = 1 - c
e = b * d
f = a + e 
g = 1 - f
h = 0 / 60
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 11 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 385
Rationale: "ans : 385 7 c 1 * 11 c 2 answer e )"
Answer: e
Python program:
a = 11 * 3
b = a * 7
Problem: in the year 1990 there are 5000 men 3000 women 2000 boys . in 1994 men are increased by 20 % women are increased by ratio of boys and women ?
Options: a ) 11000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 15000
Rationale: total population in year 1990 = 5000 + 3000 + 2000 = 10000 total population in year 1994 = ( ( 5000 * 120 / 100 ) + ( 3000 + ( 3000 * 2 / 3 ) ) + ( 2000 ) ) = 13000 answer : c
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 5000 * b
d = 2000 / 3000
e = 1 + d 
f = 3000 * e
g = c + f 
h = g + 2000
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b
Options: a ) 10 , b ) 8 , c ) 6 , d ) 5 , e ) 7
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 . hence , b ' s age = 2 x = 10 years answer : a"
Answer: a
Python program:
a = 27 - 2
b = a * 2
c = 4 + 1 
d = b / c
Problem: what is the sum of the multiples of 4 between 13 and 125 inclusive ?
Options: a ) 1,890 , b ) 1,960 , c ) 2,200 , d ) 3,780 , e ) 4,400
Rationale: "the first multiple of 12 between 13 and 125 is 16 while the last is 124 total number of terms is given by 124 = 16 + ( n - 1 ) 4 4 n - 4 = 108 n = 112 / 4 = 28 or , ( 124 - 16 ) / 4 + 1 = 28 so , we have 28 multiples of 12 between 13 and 125 sum = 14 ( 2 * 16 + ( 27 ) 4 ) = 14 ( 140 ) = 1960 answer : b"
Answer: b
Python program:
a = 125 - 3
b = 13 + 2 
c = a + b 
d = c / 2
e = 125 - 3
f = 13 + 2 
g = e - f
h = g / 4
i = h + 1 
j = d * i
Problem: the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate s , in cubic meters per minutes , at which the water is flowing into the swimming pool ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.5 , d ) 0.75 , e ) not enough information to determine the rate
Rationale: "the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e"
Answer: e
Python program:
a = 840 / 0
Problem: four horses are tethered at 4 corners of a square field of side 70 metres so that they just can not reach one another . the area left ungrazed by the horses is :
Options: a ) 1050 sq . m
b ) 3850 sq . m
c ) 950 sq . m
d ) 1075 sq . m
e ) 1065 sq . m
Rationale: area ungrazed is given by total area - 4 * area grazed by each horse = 70 * 70 - 4 * ( 90 / 360 ) * pi * ( 70 / 2 ) ^ 2 as the angle made by the horse is 90 degree , so applying the area of the sector , = theta / 360 * pi * radius ^ 2 above = 70 * 70 - pi * ( 70 / 2 ) * ( 70 / 2 ) = 70 * 70 { 1 - pi / 4 } = 70 * 70 { 6 / ( 7 * 4 ) } , expanding pi = 22 / 7 = ( 70 * 70 * 6 ) / ( 7 * 4 ) = 1050 sq m answer : a
Answer: a
Python program:
a = square_area - (
Problem: a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 38 . find the profit percentage ?
Options: a ) 80 % , b ) 90 % , c ) 59 % , d ) 40 % , e ) 53 %
Rationale: l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 190 ( 30 * 5 ) profit percentage = ( 190 - 100 ) / 100 * 100 = 90 % answer : b
Answer: b
Python program:
a = 4 + 1 
b = 38 * a
c = 25 * 4
d = b - c
Problem: redo ’ s manufacturing costs for sets of horseshoes include a $ 10000 initial outlay , and $ 20 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 4500 , b ) $ 3500 , c ) $ 5500 , d ) $ 5000 , e ) $ 6300
Rationale: total manufacturing cost = 10000 + 500 * 20 = 20000 total selling cost = 500 * 50 = 25000 profit = 25000 - 20000 = 5000 answer : d
Answer: d
Python program:
a = 50 - 20
b = a * 500
c = b - 10000
Problem: from below option 50 is divisible by which one ?
Options: a ) 3 , b ) 2 , c ) 7 , d ) 8 , e ) 9
Rationale: "50 / 2 = 25 b"
Answer: b
Python program:
a = math.sqrt(50)
Problem: in n is a positive integer less than 200 , and 24 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 24 n / 60 must be an integer . = > 2 n / 5 must be an integer . hence n must be a multiple of 5 . = > n has 1 different prime integers ."
Answer: a
Python program:
a = 1 + 4 
b = 60 / 2
c = b / 2
d = c / 3
e = a / d
f = e + 2
Problem: on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 4 cups of tea . last week mo drank a total of 42 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 42 t - c = 14 - > t = 28 . c = 14 . mo drinks 4 cups of tea a day then number of days that are not rainy = 28 / 4 = 7 so number of rainy days = 7 - 7 = 0 a is the answer ."
Answer: a
Python program:
a = 4 + 4 
b = 42 + 14 
c = b / 2
d = c / 4
e = a - d
Problem: 469157 * 9999
Options: a ) 1691100843 , b ) 4591100843 , c ) 4691100843 , d ) 3691100843 , e ) none of these
Rationale: "explanation : 469157 * ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 option c"
Answer: c
Python program:
a = 469157 / 9999
b = a * 100
Problem: what is the largest 4 digit number exactly divisible by 72 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9936
Rationale: "largest 4 digit number = 9999 9999 ÷ 72 = 138 , remainder = 63 hence largest 4 digit number exactly divisible by 88 = 9999 - 63 = 9936 answer : e"
Answer: e
Python program:
a = 10 ** 4
b = a / 72
c = math.floor(b)
d = c * 72
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 360 and for 36 kgs of apples is 420 then the cost of first 25 kgs of apples is
Options: a ) 100 , b ) 250 , c ) 125 , d ) 110 , e ) 115
Rationale: "ans : by framing equations we get 30 l + 3 q = 360 30 l + 6 q = 420 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 10 cost of 10 kgs of apples = 25 x 10 = 250 answer : b"
Answer: b
Python program:
a = 33 - 30
b = 420 - 360
c = 36 - 33
d = b / c
e = a * d
f = 360 - e
g = f / 30
h = g * 25
Problem: if x = 3 ^ 27 and x ^ x = 3 ^ k , what is k ?
Options: a ) 3 ^ 9 , b ) 3 ^ 12 , c ) 3 ^ 27 , d ) 3 ^ 30 , e ) 3 ^ 33
Rationale: "solution : we know that x = 3 ^ 27 which implies x ^ x = ( 3 ^ 27 ) ^ ( 3 ^ 27 ) = 3 ^ ( 27 * 3 ^ 27 ) [ because ( x ^ y ) ^ z = x ^ ( y * z ) ) ] so 3 ^ ( 3 ^ 3 * 3 ^ 27 ) = 3 ^ ( 3 ^ ( 3 + 27 ) ) [ because x ^ a * x ^ b = x ^ ( a + b ) ] therefore x ^ x = 3 ^ ( 3 ^ 30 ) given that x ^ x = 3 ^ k so 3 ^ ( 3 ^ 30 ) = 3 ^ k since the base is same the exponent will also be same therefore k = 3 ^ 30 answer : d"
Answer: d
Python program:
a = 3 ** 27
b = a * 27
Problem: find the least number which when divided by 5,6 , 7,8 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: "l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )"
Answer: d
Python program:
a = math.lcm(5, 6)
b = 3 + a
Problem: the ratio of the radius of two circles is 3 : 4 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 9 : 16 , c ) 1 : 9 , d ) 3 : 7 , e ) 3 : 4
Rationale: "r 1 : r 2 = 3 : 4 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 9 : 16 answer : b"
Answer: b
Python program:
a = circle_area / (
Problem: evaluate : 30 - | - x + 6 | for x = 10
Options: a ) 16 , b ) 26 , c ) 36 , d ) 46 , e ) 56
Rationale: substitute x by 10 in the given expression and evaluate 30 - | - ( 10 ) + 6 | = 30 - | - 10 + 6 | = 30 - | - 4 | = 30 - 4 = 26 correct answer b ) 26
Answer: b
Python program:
a = negate + ( 
b = 30 - negate
Problem: in a partnership , a invests 1 ⁄ 6 of the capital for 1 ⁄ 6 of the time , b invests 1 ⁄ 3 of the capital for 1 ⁄ 3 of the time and c , the rest of the capital for whole time . find a ’ s share of the total profit of 2300
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) none of these
Rationale: remaining capital = 1 - ( 1 ⁄ 6 + 1 ⁄ 3 ) = 1 ⁄ 2 ratio of their profit = 1 ⁄ 6 × [ 1 ⁄ 6 × 12 ] : 1 ⁄ 3 × [ 1 ⁄ 3 × 12 ] : 1 ⁄ 2 × 12 = 1 ⁄ 3 : 4 ⁄ 3 : 6 = 1 : 4 : 18 ∴ a ' s share = 1 / 1 + 4 + 18 × 2300 = 100 answer a
Answer: a
Python program:
a = 6 * 3
b = 1 + 4 
c = a + b 
d = 1/(c)
e = d * 2300
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 50 % at 30 % profit . find his % profit on total .
Options: a ) 23 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "if the total quantity was 100 then 40 x 20 % + 50 x 30 % = 23 this profit will remain same for any total quantity unless the % of products remains the same . hence ' a ' is the answer"
Answer: a
Python program:
a = 280 * 40
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = 280 * 50
g = f / 100
h = 100 + 30 
i = h / 100
j = g * i
k = e + j 
l = k - 280
m = l * 100
n = m / 280
Problem: car x began traveling at an average speed of 35 miles per hour . after 48 minutes , car y began traveling at an average speed of 39 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 48 minutes , car x travels 28 miles . car y gains 4 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."
Answer: e
Python program:
a = 48 / const_60
b = a * 35
c = 39 - 35
d = b / c
e = 35 * d
Problem: how many 4 - digit positive integers are there in which all 4 digits are even ?
Options: a ) 625 , b ) 600 , c ) 500 , d ) 400 , e ) 256
Rationale: "positive integers - 2 , 4,6 , 8,0 let the integers of a four digit positive number be abcd a can take four values ( 2,4 , 6,8 ) b can take five values ( 0 , 2,4 , 6,8 ) c can take five values ( 0 , 2,4 , 6,8 ) d can take five values ( 0 , 2,4 , 6,8 ) the total is 5 * 5 * 5 * 4 the answer according to me is 500 answer : c"
Answer: c
Python program:
a = 4 + 4 
b = 4 + 4 
c = a * b
d = 4 + 4 
e = 4 * 4
f = d * e
g = c * f
Problem: benny goes to the market for buying some apples to be distributed between her 9 kids equally . she takes 360 dollars with her . the cost of each apple is 4 dollars . how many apples does she buy to share them equally between her eighteen kids ?
Options: a ) 8 , b ) 9 , c ) 5 , d ) 7 , e ) 10
Rationale: cost of each apple = 4 dollars apples that benny can buy with the amount she has = 360 / 4 = 90 . apples that each kid gets evenly = 90 / 18 = 5 apples . so the answer is c = 5
Answer: c
Python program:
a = 360 / 4
b = 9 * 2
c = a / b
Problem: it takes nine minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?
Options: a ) 13.58 , b ) 13.87 , c ) 14.24 , d ) 14.59 , e ) 14.85
Rationale: the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 9 ) = 1 / 540 of the video per second . the combined rate is 1 / 15 + 1 / 540 = 37 / 540 of the video per second . the time required to load the video is 540 / 37 = 14.59 seconds . the answer is d .
Answer: d
Python program:
a = 2 + 3 
b = a + 4 
c = b * const_60
d = 1/(c)
e = 3 * 4
f = e + 3 
g = 1/(f)
h = d + g 
i = 1/(h)
j = 4 * 4
k = j * 3
l = k - 2
m = 100 * 100
n = l / m
o = i - n
Problem: a sum of money invested at compound interest to rs . 800 in 3 years and to rs 820 in 4 years . the rate on interest per annum is .
Options: a ) 0.4 % , b ) 5.0 % , c ) 2.5 % , d ) 7 % , e ) 8 %
Rationale: explanation : s . i . on rs 800 for 1 year = 20 rate = ( 100 * 20 ) / ( 800 * 1 ) = 2.5 % answer : c
Answer: c
Python program:
a = 820 - 800
b = 100 * a
c = b / 800
Problem: if two positive numbers are in the ratio 1 / 9 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 60 % . , d ) 28.6 % . , e ) 80 % .
Rationale: "given ratio = 1 / 9 : 1 / 7 = 7 : 9 let first number be 7 x and the second number be 9 x . the second number is more than first number by 2 x . required percentage = 2 x / 7 x * 100 = 28.6 % . answer : d"
Answer: d
Python program:
a = 1 / 7
b = a * 100
Problem: find compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually
Options: a ) rs 312 , b ) rs 412 , c ) rs 512 , d ) rs 612 , e ) none of these
Rationale: explanation : please apply the formula amount = p ( 1 + r 100 ) nc . i . = amount - p answer : d
Answer: d
Python program:
a = 7500 * 4
b = a / 100
c = 7500 + b 
d = 7500 * 4
e = d / 100
f = 7500 + e 
g = f * 4
h = g / 100
i = c + h 
j = i - 7500
Problem: the front wheels of a wagon are 2 π feet in circumference and the rear wheels are 3 π feet in circumference . when the front wheels have made 10 more revolutions than the rear wheels , how many feet has the wagon travelled ?
Options: a ) 30 π , b ) 45 π , c ) 60 π , d ) 90 π , e ) none
Rationale: solution let the rear wheel make x revolutions . then , the front wheel makes ( x + 10 ) revolutions . ( x + 10 ) x 3 π = x × 2 π ‹ = › 3 x + 30 = 2 x ‹ = › x = 30 . distance travelled by the wagon = ( 2 π x 30 ) ft ‹ = › ( 60 π ) ft . answer c
Answer: c
Python program:
a = 2 * 10
b = a * 3
c = 12 - 1
d = c * 2
e = b * d
f = 3 + 4 
g = e / f
Problem: lcm of two numbers is 7700 and hcf is 11 . if one number is 308 then other number is
Options: a ) 269 , b ) 285 , c ) 300 , d ) 275 , e ) none of these
Rationale: option d
Answer: d
Python program:
a = 7700 * 11
b = a / 308
Problem: a car is running at a speed of 80 kmph . what distance will it cover in 20 sec ?
Options: a ) 100 m , b ) 440 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: speed = 80 kmph = 80 * 5 / 18 = 22 m / s distance covered in 20 sec = 22 * 10 = 440 m answer is b
Answer: b
Python program:
a = 80 / const_3_6
b = a * 20
Problem: a , b , c subscribe rs . 50,000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35,000 , a receives
Options: a ) rs . 8400 , b ) rs . 11,900 , c ) rs . 13,600 , d ) rs . 14,700 , e ) none
Rationale: "solution : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 . = > 3 x = 36000 . = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . so a ' s share = rs . ( 35000 x 21 / 50 ) = rs . 14,700 . answer : option d"
Answer: d
Python program:
a = 10 * 5000
b = a - 5000
c = 4000 + 5000 
d = b - c
e = d / 3
f = 4000 + 5000 
g = e + f 
h = 10 * 5000
i = g / h
j = 3 + 4 
k = j * 5000
l = i * k
m = l / 1000
n = math.floor(m)
o = n - 1
Problem: a charitable association sold an average of 66 raffle tickets per member . among the female members , the average was 70 raffle tickets . the male to female ratio of the association is 1 : 2 . what was the average number r of tickets sold by the male members of the association
Options: a ) 50 , b ) 56 , c ) 58 , d ) 62 , e ) 66
Rationale: "given that , total average r sold is 66 , male / female = 1 / 2 and female average is 70 . average of male members isx . ( 70 * f + x * m ) / ( m + f ) = 66 - > solving this equation after substituting 2 m = f , x = 58 . ans c ."
Answer: c
Python program:
a = 1 + 2 
b = 66 * a
c = 70 * 2
d = b - c
Problem: a train 880 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 540 , c ) 500 , d ) 420 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 880 + x ) / 60 = 65 / 3 x = 420 m . answer : option d"
Answer: d
Python program:
a = 78 - 1
b = a * const_0_2778
c = 880 / b
Problem: if x is less than y by 50 % then y exceed x by :
Options: a ) 33.33 % , b ) 100 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 50 ( 100 - 50 ) * 100 = 100 % answer : b"
Answer: b
Python program:
a = 100 - 50
b = 100 / a
c = b - 1
d = c * 100
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 30 % profit ?
Options: a ) 66.3 , b ) 76.3 , c ) 86.3 , d ) 16.3 , e ) 36.3
Rationale: "explanation : c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 130 % of rs . 630 = 130 / 100 * 630 = rs . 819 . s . p . per kg = 819 / 50 = rs . 16.38 = 16.30 . answer : d"
Answer: d
Python program:
a = 30 * 11
b = 20 * 14
c = a + b 
d = 30 * 11
e = 20 * 14
f = d + e 
g = f / 100
h = g * 30
i = c + h 
j = 30 + 20 
k = i / j
Problem: what was the principal , if at 5 % per annum the interest after 10 years amounted to rs . 3100 less than the sum lent ?
Options: a ) 6200 , b ) 3000 , c ) 3000 , d ) 2000 , e ) 1000
Rationale: "p - 2336 = ( p * 10 * 5 ) / 100 p = 6200 answer : a"
Answer: a
Python program:
a = 5 * 10
b = a / 100
c = 1 - b
d = 3100 / c
Problem: the list price of an article is rs . 68 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 3.23 % , b ) 4.23 % , c ) 5.23 % , d ) 7.23 % , e ) 8.23 %
Rationale: "68 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 8.23 % answer : e"
Answer: e
Python program:
a = 10 / 100
b = 68 * a
c = 68 - b
d = c - 56
e = 10 / 100
f = 68 * e
g = 68 - f
h = d / g
i = h * 100
Problem: the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 square feet , how much will it cost to paint outside of a cube having 8 feet each side .
Options: a ) rs . 850 , b ) rs . 860 , c ) rs . 876 , d ) rs . 886 , e ) none of these
Rationale: "explanation : we will first calculate the surface area of cube , then we will calculate the quantity of paint required to get answer . here we go , surface area = 6 a 2 = 6 ∗ 8 ( 2 ) = 384 sq feet quantity required = 38416 = 24 kg cost of painting = 36.50 ∗ 24 = rs . 876 option c"
Answer: c
Python program:
a = surface_cube / (
b = a * 16