euclaise/mathqa_programs huggingface dataset:
Problem: calculate the area of a triangle , if the sides are 13 cm , 12 cm and 5 cm , what is its area ?
Options: a ) 36 cm 2
b ) 35 cm 2
c ) 30 cm 2
d ) 32 cm 2
e ) 31 cm 2
Rationale: the triangle with sides 13 cm , 12 cm and 5 cm is right angled , where the hypotenuse is 13 cm . area of the triangle = 1 / 2 * 12 * 5 = 30 cm 2 answer : c
Answer: c
Python program:
a = 12 / 2
b = a * 5
Problem: 1 , 3,5 , 7,9 , . . 50 find term of sequnce for this .
Options: a ) 1356 , b ) 1557 , c ) 1688 , d ) 1700 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Python program:
a = negate - (
Problem: if a ^ 2 + b ^ 2 = 177 and ab = 54 then find the value of a + b / a - b ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 117 + 2 * 24 = 225 a + b = 15 ( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 117 - 2 * 54 a - b = 3 a + b / a - b = 15 / 3 = 5 answer is c ."
Answer: c
Python program:
a = math.sqrt(177)
b = a * 10
c = b + 3
Problem: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 210 pounds of the mixture ?
Options: a ) 150 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 210 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 210 = 150 pounds answer ( a )"
Answer: a
Python program:
a = 5 * 210
b = 5 + 2 
c = a / b
Problem: the simple interest on a sum of money will be rs . 1200 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 2400 , e ) 1732
Rationale: "p - - - 10 - - - - 1200 p - - - 5 - - - - - 600 3 p - - - 5 - - - - - 1800 - - - - - - = > 2400 answer : d"
Answer: d
Python program:
a = 1200 / 10
b = a * 5
c = b * 3
d = 1200 / 10
e = d * 5
f = c + e
Problem: pipe p can drain the liquid from a tank in 4 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 8 / 23 , c ) 3 / 4 , d ) 17 / 29 , e ) 3 / 8
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 4 / 4 ) rq ] = 4 / 4 = 1 also , rp = rr / ( 2 / 3 ) = > 1 = rr / ( 2 / 3 ) = > rr = 2 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 1 + 2 / 3 = 8 / 3 = 1 / ( 3 / 8 ) thus running simultaneously , pipe q will drain 3 / 8 of the liquid . thus answer = e ."
Answer: e
Python program:
a = 3 * 0
b = 4 * 4
c = b * 2
d = 4 * 4
e = c + d 
f = a / e
Problem: a number whose fifth part increased by 4 is equal to its fourth part diminished by 4 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 220 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 4 = ( n / 4 ) - 4 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 8 â ‡ ’ ( 5 n - 4 n ) / 20 = 8 â ˆ ´ n = 160 option : a"
Answer: a
Python program:
a = 4 + 4 
b = 1 / 4
c = 1 + 4 
d = 1 / c
e = b - d
f = a / e
Problem: a , b , c together can earn $ 600 per day . while a and c together earn $ 400 and b and c together can earn $ 300 . the daily earnings of c ?
Options: a ) $ 100 , b ) $ 200 , c ) $ 250 , d ) $ 300 , e ) $ 500
Rationale: b ' s daily earnings = 600 - 400 = $ 200 a ' s daily earnings = 600 - 300 = $ 300 c ' s daily earnings = 600 - 200 - 300 = $ 100 answer is a
Answer: a
Python program:
a = 600 - 400
b = 300 - a
Problem: a can do a piece of work in 3 days of 5 hours each and b alone can do it in 5 days of 3 hours each . how long will they take it to do working together 3 / 4 hours a day ?
Options: a ) 6 days , b ) 5 days , c ) 10 days , d ) 9 days , e ) 8 days
Rationale: a ' s work per hour = 1 / 15 b ' s work per hour = 1 / 15 a & b ' s work per hour together = ( 1 / 15 ) + ( 1 / 15 ) = 2 / 15 so a & b together complete the work in 15 / 2 hours . . . if they work 2 1 / 2 = 5 / 2 hours a day , it will take ( 15 / 2 ) / ( 3 / 4 ) days = 10 days . . . answer : c
Answer: c
Python program:
a = 3 * 5
b = 1 / a
c = 3 * 5
d = 1 / c
e = b + d 
f = 1 / e
g = 3 / 4
h = f / g
Problem: if the price of a certain bond on may 1 st was 3 / 4 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 114.28 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 3 / 4 * 12 = 9 ; the price on july 1 st = 8 * 1.5 = 12 . the average price of the bond on may 1 st and july 1 st = ( 9 + 12 ) / 2 = 10.5 . the price of the bond on june 1 st ( 12 ) is 24 / 21 times ( 114.28 % ) the average price of the bond on may 1 st and july 1 st . answer : b .
Answer: b
Python program:
a = 50 * const_0_33
b = 100 + const_0_33 
c = a + b
Problem: a 300 m long train crosses a platform in 40 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 367 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 40 = 50 / 3 3 x + 900 = 2000 = > x = 367 m . answer : d"
Answer: d
Python program:
a = speed * (
b = a - 40
Problem: the average age of a class of 25 students is 26 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 40 , b ) 41 , c ) 52 , d ) 62 , e ) 73
Rationale: "total age of all students = 25 ã — 26 total age of all students + age of the teacher = 26 ã — 27 age of the teacher = 27 ã — 26 â ˆ ’ 25 ã — 26 = 26 ( 27 â ˆ ’ 25 ) = 26 ã — 2 = 52 answer is c ."
Answer: c
Python program:
a = 25 + 1 
b = 26 + 1 
c = a * b
d = 25 * 26
e = c - d
Problem: the difference between two numbers is 1356 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is
Options: a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 340
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 smaller number = 270 answer : b"
Answer: b
Python program:
a = 1356 - 15
b = 6 - 1
c = a / b
Problem: on a test , the boys in the class averaged 90 points and the girls in the class averaged 96 points . if the overall class average was 94 points , what is the ratio of boys to girls in the class ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
Rationale: ( 96 g + 90 b ) / ( g + b ) = 94 96 g + 90 b = 94 ( g + b ) 2 g = 4 b b / g = 1 / 2 the answer is a .
Answer: a
Python program:
a = 96 - 94
b = 94 - 90
c = a / b
Problem: 9 - 3 ÷ 1 / 3 + 3 = ?
Options: a ) 1 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: 9 - 3 1 / 3 + 3 = 9 - 3 ÷ 1 / 3 + 3 = 9 - ( 3 x 3 ) + 3 = 9 - 9 + 3 = 3 correct answer : b
Answer: b
Python program:
a = 1 / 3
b = 3 / a
c = 9 - b
d = c + 3
Problem: if n divided by 7 has a remainder of 2 , what is the remainder when 5 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 2 for some integer p hence 5 n = > 35 q + 10 = > remainder = > 10 for some integer q alternatively = > n = 2 > 5 n = > 10 = > 10 divided by 7 will leave a remainder 3 hence c"
Answer: c
Python program:
a = 5 * 2
Problem: in the coordinate plane , points ( x , 2 ) and ( 8 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 8 , b ) 6 , c ) 5 , d ) 3 , e ) 2
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 8 , y ) = ( 8,4 ) - - > x + y = 4 + 4 = 8 . answer : a"
Answer: a
Python program:
a = 8 * 2
b = 2 / 2
c = a * b
Problem: find the ones digit of 73 ^ 355
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: the units digit of 73 ^ 355 will be the same as the units digit of 3 ^ 355 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 355 = 352 + 3 = ( multiple of 4 ) + 2 , then the units digit of 3 ^ 355 will be the third number in the pattern thus 7 . answer : d .
Answer: d
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 355 / 4
e = math.floor(d)
f = e * 4
g = 355 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: how long will it take a train travelling at 98 kmph to pass an electric pole if the train is 140 m long
Options: a ) 6.15 , b ) 5.15 , c ) 3.15 , d ) 1.15 , e ) 7.15
Rationale: "sol . speed = [ 98 x 5 / 18 ] m / sec = 27.2 m / sec . time taken = ( 140 / 27.2 ) sec = 5.15 sec . answer b"
Answer: b
Python program:
a = 140 / 1000
b = a / 98
c = b * 3600
Problem: a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . the speed of the car is :
Options: a ) 120 kmph , b ) 150 kmph , c ) 50 kmph , d ) 80 kmph , e ) 75 kmph
Rationale: "let speed of the car be x kmph . then , speed of the train = 150 / 100 x = 3 / 2 x kmph . 75 / x - 75 / ( 3 / 2 ) x = 125 / 10 x 60 75 / x - 50 / x = 5 / 24 x = 25 x 24 / 5 = 120 kmph . answer : a"
Answer: a
Python program:
a = 12 * 5
b = a - 1
c = 12 * 5
d = b * c
e = 4 + 1 
f = d / e
Problem: from below option 22 is divisible by which one ?
Options: a ) a ) 3 , b ) b ) 4 , c ) c ) 11 , d ) d ) 9 , e ) e ) 7
Rationale: "22 / 11 = 2 c"
Answer: c
Python program:
a = math.sqrt(22)
Problem: by approximately what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ?
Options: a ) 732 % , b ) 560 % , c ) 641 % , d ) 370 % , e ) 300 %
Rationale: "what percent is x greater than 1 / 2 if ( 1 / 2 ) ( x ) = 1 ? = > x = 2 % change = [ ( 2 - 1 / 2 ) / ( 1 / 2 ) ] * 100 = ( 4 - 1 ) * 100 = 300 % approx ans , e"
Answer: e
Python program:
a = 1 / 2
b = 2 - a
c = 1 / 2
d = b / c
e = d * 100
Problem: set x consists of all two - digit primes and set y consists of all positive multiples of 6 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 91
Rationale: "set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 6 , 12 , 18 , . . . . . . . . . . . . . . . , 84 , 90 , 96 } combining two sets , say set z set z = { 6 , 11 , 12 , 13 , 17 , 18 , . . . . . . . . . . . . . . . . . . . , 83 , 84 , 89 , 90 , 96,97 } range = max value - min value range ( z ) = 97 - 6 = 91 oa e is the answer ."
Answer: e
Python program:
a = 100 - 3
b = a - 6
Problem: if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 22.5 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 23 , 30 , 22 , 26 , 19 , 33 and 35 19 , 22 , 23 , 26 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 23 , 26 . . the median of these numbers = center of 22 and 23 = 22.5 c"
Answer: c
Python program:
a = 23 + 26 
b = a / 2
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 800 * ( 25 / 100 ) = 200 - - - - 5 ? - - - - 1 = > rs . 40"
Answer: a
Python program:
a = 800 * 25
b = a / 100
c = b / 5
Problem: 37 . if the cost price of 15 tables be equal to the selling price of 20 tables , the loss per cent is ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 37.5 % , e ) 38 %
Rationale: let c . p . of each table = re . 1 c . p . of 20 tables = rs . 20 s . p . of 20 table = c . p . of 15 tables = rs . 15 loss = ( 5 / 20 ) x 100 % = 25 % answer : c
Answer: c
Python program:
a = 20 - 15
b = a / 20
c = b * 100
Problem: the number 46 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 10 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 46 : 1 , 4 , 9 , 16 , 25 , 36 . now , 46 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 46 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 46 equals to 1 + 9 + 36 = 1 ^ 2 + 3 ^ 2 + 6 ^ 2 = 46 - - > 1 + 3 + 6 = 10 . answer : d ."
Answer: d
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: in a certain circle there are 9 points . what is the number of the triangles connecting 4 points of the 9 points ?
Options: a ) 80
b ) 96
c ) 108
d ) 126
e ) 132
Rationale: imo : d here we have to select 4 points out of 9 points . order is not important so the answer will be 9 c 4 = 126 answer d
Answer: d
Python program:
a = math.factorial(9)
b = 10 / 2
c = math.factorial(b)
d = math.factorial(4)
e = c * d
f = a / e
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 5 % per first year and 6 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5565 , d ) 1976 , e ) 1671
Rationale: "5000 * 105 / 100 * 106 / 100 = > 5565 answer : c"
Answer: c
Python program:
a = 100 + 5 
b = 5000 * a
c = b / 100
d = 100 + 6 
e = c * d
f = e / 100
Problem: how many trailing zeroes does 49 ! + 50 ! have ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 22
Rationale: "49 ! + 50 ! = 51 * 49 ! no of trailing 0 ' s = no of 5 * 2 no of 2 ' s = 49 / 2 + 49 / 4 + 49 / 8 + 49 / 16 + 49 / 32 = d no of 5 ' s = 49 / 5 + 49 / 25 = 10 = p now since p < d no of trailing 0 ' s = 10 answer : b"
Answer: b
Python program:
a = 50 + 1 
b = 1 + 4 
c = a / b
d = c + 2
Problem: a club wants to mix 30 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 30 * 8 + 5 * w ) / ( 30 + w ) = > 180 + 6 w = 240 + 5 w = > w = 60 answer d"
Answer: d
Python program:
a = 30 * 8
b = 6 * 0
c = a - b
Problem: the sum of the ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 = > x = 8 . age of youngest child = x = 8 years . answer : d"
Answer: d
Python program:
a = 5 / 3
b = 70 / a
c = 5 - 1
d = c * 3
e = b - d
f = e / 3
Problem: rs . 1070 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) rs . 190 , b ) rs . 260 , c ) rs . 493 , d ) rs . 393 , e ) rs . 593
Rationale: "a + b + c = 1070 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1070 = rs . 493 answer : c"
Answer: c
Python program:
a = 4 + 2 
b = a + 3 
c = 1070 / b
d = 4 * c
Problem: nancy obtained 66 , 75 , 52 , 68 and 89 marks ( out of 100 ) in american literature , history , home economics , physical education and art . calculate her average marks ?
Options: a ) 50 , b ) 80 , c ) 70 , d ) 60 , e ) 71
Rationale: explanation : average = ( 66 + 75 + 52 + 68 + 89 ) / 5 = 70 . answer : c ) 70
Answer: c
Python program:
a = 66 + 75 
b = a + 52 
c = b + 68 
d = c + 89 
e = 4 + 1 
f = d / e
Problem: the difference between the local value and the face value of 7 in the numerical 32675149 is
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of them
Rationale: "= ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 answer is d"
Answer: d
Python program:
a = 7 * 1000
b = a - 7
Problem: the average of numbers 0.64206 , 0.64207 , 0.64208 and 0.64209 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642075 , e ) none
Rationale: "answer average = ( 0.64206 + 0.64207 + 0.64208 + 0.64209 ) / 4 = 2.5683 / 4 = 0.642075 correct option : d"
Answer: d
Python program:
a = 0 * 64206
b = 0 * 64206
c = a + b 
d = c / 0
Problem: a textile manufacturing firm employees 80 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 80 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 4375 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 79 / 80 ) â ˆ ’ 150000 ã — ( 79 / 80 ) â ˆ ’ 75000 . = > rs 2 , 70,625 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,625 = > rs . 4,375 answer : d"
Answer: d
Python program:
a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000 
e = b - d
f = 80 - 1
g = f / 80
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 80 - 1
m = l / 80
n = k * m
o = j - n
p = o - 75000
q = e - p
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 12 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 12 = 1 km . the time it takes the hiker to complete this distance is 1 / 4 hours = 15 minutes the cyclist needs to wait 15 - 5 = 10 minutes the answer is a ."
Answer: a
Python program:
a = 5 / const_60
b = 12 * a
c = 5 / const_60
d = 4 * c
e = b - d
f = e / 4
g = f * const_60
Problem: a milk man has 30 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 35 % , e ) none of these
Rationale: explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 30 liters of milk . therefore , profit percentage = 35 % . answer : d
Answer: d
Python program:
a = 20 + 5 
b = a + 10 
c = 5 / 2
d = c + 3 
e = b + d 
f = e * 18
g = 30 * 18
h = f - g
i = 30 * 18
j = h / i
k = j * 100
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 180 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 900 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 180 geese survived the first year : 1 / 5 * ( total ) = 180 - - > ( total ) = 900 . answer : d ."
Answer: d
Python program:
a = 3 / 5
b = 1 - a
c = 180 / b
d = 3 / 4
e = c / d
f = 2 / 3
g = e / f
Problem: 20 litres of mixture of acid and water contain 10 % water . how much water should be added so that percentage of water becomes 20 % in this mixture ?
Options: a ) 2 l , b ) 3 l , c ) 2.5 l , d ) 4 l , e ) 5 l
Rationale: total mixture = 20 ltr water contain = 10 % of 20 ltr = > 2 ltr water it means 18 ltr is acid in that mixture we have to make 20 % water so . . 20 % of 20 = 4 ltr water must be there in the new mixture we have already 2 ltr water so we have to add 2 ltr more answer : a
Answer: a
Python program:
a = 10 / 100
b = 20 * a
Problem: what will be the remainder when 8 - 3 + 3 ^ 5 + 2 ^ 10 is divided by 4 ?
Options: a ) 12 , b ) 3 , c ) 16 , d ) 0 , e ) 9
Rationale: "the multiplication ( e . g . 2 ^ 10 ) is done first and then the sum ( e . g . 15 + 20 ) and subtraction ( e . g . 8 - 3 ) , and after all this expression it should be divided by 4 and the answer is 0 , option d ."
Answer: d
Python program:
a = 3 - 8
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 64 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 8 : 3 , c ) 8 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 64 : √ 9 = 8 : 3 answer : b
Answer: b
Python program:
a = math.sqrt(64)
b = math.sqrt(9)
c = a / b
Problem: a trader bought a car at 15 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 119 , b ) 110 , c ) 112 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 85 s = 85 * ( 140 / 100 ) = 119 100 - 119 = 19 % answer : a"
Answer: a
Python program:
a = 100 - 15
b = 100 + 40 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: the ratio between the present ages of a and b is 6 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 5 : 4 , b ) 3 : 0 , c ) 5 : 1 , d ) 3 : 2 , e ) 3 : 7
Rationale: "let the present ages of a and b be 6 x and 3 x years respectively . then , ( 6 x - 4 ) / ( 3 x + 4 ) = 1 / 1 3 x = 8 = > x = 2.67 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 20 : 4 = 5 : 1 . answer : c"
Answer: c
Python program:
a = 6 + 6 
b = 6 - 3
c = a / b
d = 6 * c
e = d + 6 
f = 6 + 6 
g = 6 - 3
h = f / g
i = 3 * h
j = i - 6
k = e / j
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 225 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1000 , b ) 1500 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "90 % 105 % - - - - - - - - 15 % - - - - 225 100 % - - - - ? = > rs . 1500 answer : b"
Answer: b
Python program:
a = 225 * 100
b = 100 + 5 
c = 100 - 10
d = b - c
e = a / d
Problem: in what time will a train 60 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 60 / 40 = 1.5 sec . answer : e"
Answer: e
Python program:
a = 144 * const_0_2778
b = 60 / a