euclaise/mathqa_programs huggingface dataset:
Problem: a 280 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
Options: a ) 230 , b ) 288 , c ) 267 , d ) 256 , e ) 220
Rationale: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 280 ) / 9 = 500 / 9 = > x = 220 . answer : e"
Answer: e
Python program:
a = 120 + 80 
b = a * const_0_2778
c = b * 9
d = c - 280
Problem: an escalator moves towards the top level at the rate of 12 ft . sec and its length is 150 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 10 sec , b ) 20 sec , c ) 15 sec , d ) 16 sec , e ) 14 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 150 / ( 12 + 3 ) = 10 sec answer : a"
Answer: a
Python program:
a = 12 + 3 
b = 150 / a
Problem: in a 100 m sprint race kelly was given a 3 m head start by abel . if abel lost the race to kelly by a distance of 0.50 m , how many meters more would abel need to overtake kelly ?
Options: a ) 20.5 , b ) 18.4 , c ) 17.5 , d ) 19.9 , e ) 21.5
Rationale: distance abel ran before completion of race - - - 100 m - 0.50 m = 99.5 m distance gained on kelly over 99.5 m - - - 3 m - 0.50 m = 2.50 m then abel gains 99.5 m / 2.50 m = 1 m on kelly every 39.8 meters . therefore 39.8 divided by half a meter ( i . e the 0.50 m abel was defeated with ) answer : d . 19.9 m
Answer: d
Python program:
a = 100 - 0
b = 100 - 0
c = 100 - 3
d = b - c
e = a / d
f = e * 0
Problem: the volume of a wall , 5 times as high as it is broad and 8 times as long as it is high , is 12.8 cu . meters . find the breadth of the wall .
Options: a ) 40
b ) 29
c ) 28
d ) 27
e ) 12
Rationale: explanation : let the breadth of the wall be x metres . then , height = 5 x metres and length = 40 x metres . x * 5 x * 40 x = 12.8 = > \ inline \ fn _ jvn x ^ 3 = \ frac { 12.8 } { 200 } = \ frac { 128 } { 2000 } = \ frac { 64 } { 1000 } = > \ inline \ fn _ jvn x = \ frac { 4 } { 10 } m = > \ inline \ fn _ jvn x = \ frac { 4 } { 10 } \ times 100 = 40 cm answer : a ) 40 cm
Answer: a
Python program:
a = 5 * 8
b = a * 5
c = 12 / 8
d = 4 / 10
e = c / d
f = 4 / 10
g = e / f
h = g * 100
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation h of the mean , what percent of the distribution is less than m + h ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + h 34 % ________________________________________________ m 34 % ________________________________________________ m - h 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - h and 16 % lie above m + h now below m + h = 16 + 34 + 34 = 84 % hence d"
Answer: d
Python program:
a = 100 - 68
b = a / 2
c = 100 - b
Problem: what is the 4 digit number whose second digit is thrice the first digit and 3 rd digit is sum of 1 st and 2 nd and last digit is thrice the second digit .
Options: a ) 2674 , b ) 1349 , c ) 3343 , d ) 3678 , e ) 3679
Rationale: let four digits is a , b , c & d . . . so by given b is 3 a c is 4 a d is 9 a so ans is 1349 answer : b
Answer: b
Python program:
a = 100 * 10
b = 1 * 3
c = b * 100
d = a + c 
e = 1 * 3
f = e + 1 
g = f * 10
h = d + g 
i = 1 * 3
j = 3 * i
k = h + j
Problem: how many of the positive factors of 20 are not factors of 24
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 20 - 1 , 2 , 4,5 , 10 , 20 factors of 24 - 1 , 2 , 3 , 4 , 6 , 8 , 12 and 24 comparing both , we have 3 factors of 20 which are not factors of 24 - 5 , 10,20 answer : b"
Answer: b
Python program:
a = 24 / 20
Problem: rs . 525 among a , b and c such that b may get 2 / 3 of a and c together get . find the share of c ?
Options: a ) 127 , b ) 150 , c ) 177 , d ) 167 , e ) 122
Rationale: a + b + c = 590 5 a = 6 b = 8 c = x a : b : c = 1 / 5 : 1 / 6 : 1 / 8 = 24 : 20 : 15 15 / 59 * 590 = rs . 150 answer : b
Answer: b
Python program:
a = 525 / 3
b = a - 100
c = b * 2
Problem: kamal obtained 81 , 68 , 82 , 69 and 90 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 81 + 68 + 82 + 69 + 90 / 5 ) = ( 390 / 5 ) = 78 . answer e"
Answer: e
Python program:
a = 81 + 68 
b = a + 82 
c = b + 69 
d = c + 90 
e = 1 + 4 
f = d / e
Problem: a farmer spent $ 33 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 36.30 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.60
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 33 = $ 13.2 on chicken feed , thus he spent the remaining 33 - 13.2 = $ 19.8 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 13.2 - - > x = $ 16.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 16.5 + 19.8 = $ 36.3 . answer : a"
Answer: a
Python program:
a = 40 / 100
b = 33 * a
c = b + 33
Problem: the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference c would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference c = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Python program:
a = 3 * 3
b = a * 40
Problem: the sum of the squares of two consecutive positive integers exceeds their product by 91 . find the integers ?
Options: a ) 9 , 10 , b ) 10 , 11 , c ) 11 , 12 , d ) 12 , 13 , e ) none of these
Rationale: let the two consecutive positive integers be x and x + 1 x 2 + ( x + 1 ) 2 - x ( x + 1 ) = 91 x 2 + x - 90 = 0 ( x + 10 ) ( x - 9 ) = 0 = > x = - 10 or 9 . as x is positive x = 9 hence the two consecutive positive integers are 9 and 10 . answer : a
Answer: a
Python program:
a = 91 - 1
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d - 1
f = e / 2
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 48 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: working backward from the day it ' s covered : day 48 : fully covered day 47 : half covered so 47 days answer : e
Answer: e
Python program:
a = 48 - 1
Problem: find compound interest on rs . 5000 at 12 % per annum for 1 year , compounded half - yearly .
Options: a ) rs . 600 , b ) rs . 618 , c ) rs . 525 , d ) rs . 620 , e ) none
Rationale: "principal = rs . 5000 , rate = 6 % per half year time = 1 year = 2 half - years amount = rs . { 5000 x ( 1 + 6 / 100 ) 2 ] = rs . [ 5000 x 53 / 50 x 53 / 50 ] = rs . 5618 c . i . = rs . ( 5618 – 5000 ) = rs . 618 answer b"
Answer: b
Python program:
a = 5000 * 12
b = a / 100
c = 5000 + b 
d = 5000 * 12
e = d / 100
f = 5000 + e 
g = f * 12
h = g / 100
i = c + h 
j = i - 5000
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 35 men in 3 days ?
Options: a ) 16 mtr . , b ) 52 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 98 mtr .
Rationale: "20 men is 6 days can build 112 metres 35 men in 3 days can build = 112 * ( 35 / 20 ) x ( 3 / 6 ) = 98 meters answer : e ."
Answer: e
Python program:
a = 35 * 3
b = 20 * 6
c = a / b
d = 112 * c
Problem: how many of the positive factors of 85 , 105 and how many common factors are there in numbers ?
Options: a ) 5 , b ) 4 , c ) 2 , d ) 3 , e ) 1
Rationale: "factors of 85 - 1 , 5 , 17 , 85 factors of 105 - 1 , 3 , 5 , 7 , 15 , 21 , 35 , 105 comparing both , we have two common factors of 85 and 105 - 1,5 answer ( c )"
Answer: c
Python program:
a = 105 / 85
Problem: sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work is ?
Options: a ) 4 days , b ) 6 days , c ) 10 days , d ) 16 days , e ) 22 days
Rationale: ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya takes x days to do the work . 5 : 4 : : 20 : x x = 4 x 20 / 5 x = 16 days . hence , tanya takes 16 days to complete the work . answer : d
Answer: d
Python program:
a = 25 / 100
b = 1 + a 
c = 20 / b
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 6 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4
Rationale: "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 6 - - > f = 12 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 12 ) = 1 / 4 . answer : e ."
Answer: e
Python program:
a = 3 * 3
b = 3 * 6
c = 2 * b
d = a / c
Problem: a and b invests rs . 4000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 3 : 5 , b ) 3 : 8 , c ) 3 : 2 , d ) 9 : 9 , e ) 3 : 1
Rationale: "( 4 * 6 + 8 * 6 ) : ( 4 * 12 ) 72 : 48 = > 3 : 2 answer : c"
Answer: c
Python program:
a = 4000 * 6
b = 4000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 4000 * e
g = d / f
Problem: find the value of x ? ( 2 / 7 ) ^ - 8 * ( 7 / 2 ) ^ - 2 = ( 2 / 7 ) ^ x
Options: a ) - 5 , b ) - 6 , c ) 4 , d ) 0 , e ) - 4
Rationale: ( 2 / 7 ) ^ - 8 * ( 7 / 2 ) ^ - 2 = ( 2 / 7 ) ^ x now , ( 7 / 2 ) ^ 8 * ( 2 / 7 ) ^ 2 = ( 2 / 7 ) ^ x on solving , ( 7 / 2 ) ^ 6 = ( 2 / 7 ) ^ x ( 2 / 7 ) ^ - 6 = ( 2 / 7 ) ^ x thus , x = - 6 . answer : b
Answer: b
Python program:
a = 7 * 7
Problem: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 200 more than the correct answer . find the number .
Options: a ) 384 , b ) 76 , c ) 26 , d ) 28 , e ) 11
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 200 25 * x / 48 = 200 x = 384 answer : a"
Answer: a
Python program:
a = 200 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
Problem: how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 18 km / hr ?
Options: a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160
Rationale: "18 km / hr = 18000 m / 3600 s = 5 m / s time = 500 / 5 = 100 seconds the answer is b ."
Answer: b
Python program:
a = 18 * const_0_2778
b = 500 / a
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 18 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 6 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 18 children ’ s 1 day ’ s work = 3 / 40 therefore , ( 10 men + 4 women + 18 children ) ’ s 1 day ’ s work = 5 / 48 + 1 / 48 + 3 / 40 = 1 / 5 the required no . of days = 5 days answer : option a"
Answer: a
Python program:
a = 24 * 10
b = 1/(a)
c = 10 * b
d = 12 * 8
e = 1/(d)
f = e * 10
g = 48 * 4
h = 1/(g)
i = h * 4
j = f + i 
k = c + j 
l = 1/(k)
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 35 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 750 ft , d ) 900 ft , e ) 1050 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 35 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 30 sub x = 30 either in ( x + 5 ) * 30 or in x * 35 to get the distance , which is 1050 . so the correct choice is e ."
Answer: e
Python program:
a = 10 / 2
b = 30 * a
c = b / 3
d = 10 / 2
e = c + d 
f = 30 * e
Problem: a frog can climb up a well at 3 ft per min but due to slipperiness of the well , frog slips down 2 ft before it starts climbing the next minute . if the depth of the well is 57 ft , how much time will the frog take to reach the top ?
Options: a ) 29 , b ) 27 , c ) 55 , d ) 17 , e ) 10
Rationale: explanation : as per given , in 1 min , frog climbs up 3 ft and slips down by 2 ft . so the frog climbs only 1 ft in 1 min so after 54 mins , it would have climbed 54 ft . at the end of 55 mins it climbs up 3 ft to make it 57 ft and come out of the well . once it had reached the destination , it will not slip . so the frog will take only 55 minutes to climb up the well . answer : c
Answer: c
Python program:
a = 3 - 2
b = 57 / a
Problem: if 50 % of x is 20 less than 5 % of 500 , then x is ?
Options: a ) 50 , b ) 100 , c ) 75 , d ) 25 , e ) 10
Rationale: 50 % of x = x / 2 ; 5 % of 500 = 5 / 100 * 500 = 25 given that , x / 2 = 25 - 20 = > x / 2 = 5 = > x = 10 . answer : e
Answer: e
Python program:
a = 5 / 100
b = 500 * a
c = b - 20
d = 50 / 100
e = c / d
Problem: a rectangular room 14 m long , 12 m broad is surrounded by a varandah , 3 m wide . find the area of the varandah ?
Options: a ) 170
b ) 180
c ) 190
d ) 210
e ) 150
Rationale: area of varandah = ( l + b + 2 p ) 2 p = ( 14 + 12 + 6 ) 6 = 180 m ( power ) 2 answer is b .
Answer: b
Python program:
a = 3 / 10
b = 2 * a
c = 14 + b 
d = 3 / 10
e = 2 * d
f = 12 + e 
g = c * f
Problem: calculate the largest 4 digit number which is exactly divisible by 98 ?
Options: a ) 9800 , b ) 9898 , c ) 9702 , d ) 9604 , e ) 9996
Rationale: largest 4 digit number is 9999 after doing 9999 ÷ 98 we get remainder 3 hence largest 4 digit number exactly divisible by 98 = 9999 - 3 = 9996 e
Answer: e
Python program:
a = 100 + 2 
b = a * 98
Problem: 20 6 years ago , a father was 3 times as old as his son . now the father is only twice as old as his son . then the sum of the present ages of the son and the father is :
Options: a ) 120 , b ) 156 , c ) 108 , d ) 105 , e ) 86
Rationale: let the present ages of the father and son be 2 x and x years respectively . then , ( 2 x - 26 ) = 3 ( x - 26 ) x = 52 . required sum = ( 2 x + x ) = 3 x = 156 years . answer is b
Answer: b
Python program:
a = 20 * 6
b = 6 * 3
c = b * 2
d = a + c
Problem: the compound and the simple interests on a certain sum at the same rate of interest for two years are rs . 11730 and rs . 10200 respectively . find the sum ?
Options: a ) rs . 17029 , b ) rs . 17028 , c ) rs . 17000 , d ) rs . 17008 , e ) rs . 17067
Rationale: "the simple interest for the first year is 10200 / 2 is rs . 5100 and compound interest for first year also is rs . 5100 . the compound interest for second year on rs . 5100 for one year so rate of the interest = ( 100 * 1530 ) / ( 5100 * 1 ) = 30 % p . a . so p = ( 100 * 10200 ) / ( 30 * 2 ) = rs . 17000 answer : c"
Answer: c
Python program:
a = 100 * 10200
b = 11730 - 10200
c = b * 100
d = 10200 / 2
e = c / d
f = e * 2
g = a / f
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 6 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 9
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 6 ^ 2 = 1 / 4 answer : c"
Answer: c
Python program:
a = 3 ** 2
b = 1 * a
c = 6 ** 2
d = b / c
Problem: each child has 3 crayons and 12 apples . if there are 6 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 18 , d ) 36 , e ) 10
Rationale: 3 * 6 = 18 . answer is c .
Answer: c
Python program:
a = 6 * 3
Problem: a man can row 6 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.79 , b ) 5.77 , c ) 5.76 , d ) 5.72 , e ) 5.71
Rationale: "m = 6 s = 1.2 ds = 7.2 us = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 d = 2.88 * 2 = 5.76 . answer : c"
Answer: c
Python program:
a = 6 + 1 
b = 6 - 1
c = a * b
d = 6 + 1 
e = 6 - 1
f = d + e 
g = c / f
h = g * 2
Problem: if the l . c . m of two numbers is 660 and their product is 18480 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18480 / 660 = 28 . answer : e
Answer: e
Python program:
a = 18480 / 660
Problem: a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is :
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) 160 m
Rationale: "explanation : let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer is d"
Answer: d
Python program:
a = 2 - 1
b = 100 * a
Problem: show timer statistics to apply for the position of photographer at a local magazine , veronica needs to include 3 or 4 of her pictures in an envelope accompanying her application . if she has pre - selected 5 photos representative of her work , how many choices does she have to provide the photos for the magazine ?
Options: a ) 5 , b ) 10 , c ) 12 , d ) 15 , e ) 50
Rationale: veronica can choose 3 photos in 5 c 3 = 10 ways she can choose 4 photos in 5 c 4 = 5 ways total number of ways = 10 + 5 = 15 answer : d
Answer: d
Python program:
a = math.factorial(5)
b = math.factorial(3)
c = 5 - 3
d = math.factorial(c)
e = b * d
f = a / e
g = math.factorial(5)
h = math.factorial(4)
i = math.factorial(1)
j = h * i
k = g / j
l = f + k
Problem: a train 300 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 ) 298 m , b ) 268 m , c ) 500 m , d ) 267 m , e ) 1000 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 300 + x ) / 60 = 65 / 3 x = 1000 m . answer : e"
Answer: e
Python program:
a = 78 - 1
b = a * const_0_2778
c = 300 / b
Problem: a consignment of 20 picture tubes contains 5 defectives . two tubes are selected one after the other at random . the probability that both are defective assuming that the first tube is not replaced before drawing the second , would be :
Options: a ) 1 / 16 , b ) 1 / 19 , c ) 1 / 4 , d ) 1 / 3 , e ) none of these
Rationale: probability of drawing a defective tube in first draw is 5 / 20 probability of drawing a defective tube in second draw ( without replacing first tube ) is 4 / 19 . therefore probability of getting both defective is = ( 5 / 20 ) * ( 4 / 19 ) = 1 / 19 answer : b
Answer: b
Python program:
a = math.comb(5, 2)
b = math.comb(20, 2)
c = a / b
Problem: two goods trains each 125 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 40 , b ) 12 , c ) 48 , d ) 51 , e ) 44
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 125 + 125 = 250 m . required time = 250 * 6 / 125 = 12 sec . answer : option b"
Answer: b
Python program:
a = 45 + 30
Problem: a sum of $ 500 amounts to 600 in 2 years at simple interest . if the interest rate is increased by 10 % it would amount to how much ?
Options: a ) $ 500 , b ) $ 700 , c ) $ 800 , d ) $ 600 , e ) $ 300
Rationale: s . i = 600 - 500 = 100 p = $ 500 t = 2 years r = 100 * 100 / 500 * 2 = 10 % new rate = 10 + 10 = 20 % new s . i . = 500 * 20 * 2 / 100 = $ 200 new amount = 500 + 200 = $ 700 answer is b
Answer: b
Python program:
a = 2 * 10
b = a / 100
c = 500 * b
d = 600 + c
Problem: if p = 775 × 778 × 781 , what is the remainder when p is divided by 14 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "p 775 / 14 leaves a remainder 5 778 / 14 leaves a remainder 8 781 / 14 leaves a remainder 11 5 * 8 * 11 = 440 so the remainder will be the remainder of 440 / 14 which is 6 ans a"
Answer: a
Python program:
a = 4 + 1 
b = 14 / a
c = 778 / b
d = c * 781
e = 4 + 1 
f = 775 / e
g = d * f
h = 100 * 3
i = g / h
Problem: the present ratio of students to teachers at a certain school is 70 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 2 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "we are given that the ratio of students to teacher is 70 to 1 . we can rewrite this using variable multipliers . students : teachers = 70 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 70 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 70 x + 50 25 x + 125 = 70 x + 50 1.667 = x x ~ 2 since x is the present number of teachers , currently there are 2 teachers . answer a ."
Answer: a
Python program:
a = 70 + 25 
b = a / 25
Problem: find out the square of a number which when doubled exceeds its one fifth by 9 ?
Options: a ) 16 , b ) 25 , c ) 19 , d ) 26 , e ) 17
Rationale: a let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 5 ) + 9 = > 10 p = p + 45 = > p = 5 p ^ 2 = 5 ^ 2 = 25 . answer : b
Answer: b
Python program:
a = 4 + 1 
b = 1 / a
c = 2 - b
d = 9 / c
e = d ** 2
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 18 , what is the total amount ?
Options: a ) 115 , b ) 116 , c ) 117 , d ) 78 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 18 39 - - - ? = > 78 answer : d"
Answer: d
Python program:
a = 100 / 45
b = a * 18
c = 50 / 45
d = c * 18
e = b + d 
f = e + 18
Problem: the l . c . m . of 2 numbers is 30 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 25 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 30 x = 5 the numbers are = 10 and 15 required sum = 10 + 15 = 25 answer is b"
Answer: b
Python program:
a = 30 * 2
b = 2 / a
c = b * 2
d = 30 * 2
e = 2 / d
f = e * 30
g = c + f
Problem: if 15 horses eat 15 bags of gram in 15 days , in how many days will one horse eat one bag of grain ?
Options: a ) 15 days , b ) 1 / 15 days , c ) 1 day , d ) 30 days , e ) 225 days
Rationale: horse * days = bags 15 * 15 = 15 and 1 * days = 1 ( 15 * 15 ) / ( 1 * days ) = 15 / 1 days = 15 answer : a
Answer: a
Python program:
a = 1/(15)
b = 1/(a)