euclaise/mathqa_programs huggingface dataset:
Problem: how much 60 % of 50 is greater than 50 % of 30 ?
Options: a ) 18 , b ) 91 , c ) 11 , d ) 17 , e ) 15
Rationale: "( 60 / 100 ) * 50 – ( 50 / 100 ) * 30 30 - 15 = 15 answer : e"
Answer: e
Python program:
a = 60 * 50
b = a / 100
c = 50 * 30
d = c / 100
e = b - d
Problem: a pair of articles was bought for $ 50 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 22.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 90 % of x = 25 x = 25 * . 9 = $ 22.50 answer is b"
Answer: b
Python program:
a = 100 - 10
b = 50 / 2
c = a * b
d = c / 100
Problem: a meal cost $ 37.25 adn there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 42 - 45 , b ) 41 - 43 , c ) 39 - 41 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 37.25 ) = 3.725 15 % ( 37.25 ) = 5.5875 total amount could have been 37.25 + 3.725 and 37.25 + 5.5875 = > could have been between 40.975 and 42.8375 = > approximately between 41 and 43 answer is b ."
Answer: b
Python program:
a = 37 * 25
b = a / 100
c = b + 37
Problem: a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ?
Options: a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km
Rationale: difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a )
Answer: a
Python program:
a = 35 * 15
b = 40 - 35
c = a / b
d = c / const_60
e = d * 40
Problem: evaluate 25 % of 450 + 45 % of 250
Options: a ) 225 , b ) 242 , c ) 252 , d ) 262 , e ) 272
Rationale: "explanation : = ( 25 / 100 ) * 450 + ( 45 / 100 ) * 250 = 225 option a"
Answer: a
Python program:
a = 450 / 25
b = 25 / a
Problem: if a lends rs . 3500 to b at 10 % p . a . and b lends the same sum to c at 11.5 % p . a . , then the gain of b ( in rs . ) in a period of 3 years is
Options: a ) rs . 154.50 , b ) rs . 155.50 , c ) rs . 156.50 , d ) rs . 157.50 , e ) none of these
Rationale: explanation : we need to calculate the profit of b . it will be , si on the rate b lends - si on the rate b gets gain of b = 3500 × 11.5 × 3 / 100 − 3500 × 10 × 3 / 100 = 157.50 option d
Answer: d
Python program:
a = 3500 * 11
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
Problem: at a certain high school , the senior class is twice the size of the junior class . if 1 / 8 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ?
Options: a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2
Rationale: start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 8 ) * 200 = 25 and ( 3 / 4 ) * 100 = 75 . 25 + 75 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : c
Answer: c
Python program:
a = 8 + 4 
b = 4 / a
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 25 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 25 % , c ) 10 % , d ) 45 % , e ) 180 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 25 percent to make square c length of each side of square c = 1.25 * 20 = 25 area of c = 25 ^ 2 = 625 difference in areas of c and cummulative areas of a and b = 625 - ( 400 + 100 ) = 225 percent is the area of square c greater than the sum of the areas of squares a and b = ( 225 / 500 ) * 100 % = 45 % answer d"
Answer: d
Python program:
a = 100 / 100
b = 1 + a 
c = 100 / 100
d = 1 + c 
e = d * 25
f = e / 100
g = b + f 
h = square_area - (
i = h - 1
j = i / 4
k = 100 / 100
l = 1 + k 
m = 1 + square_area 
n = j * m
Problem: the sum of ages of 5 children born 3 years different each is 55 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . x + 12 = 5 + 12 = 17 a"
Answer: a
Python program:
a = 3 + 4 
b = 3 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 55 
g = f / 5
Problem: there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ?
Options: a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800
Rationale: "total girls = 7 total chairs = 3 1 st chair can be occupy in 7 ways 2 nd chair can be occupy in 6 ways 3 rd chair can be occupy in 5 ways total number of ways = 7 * 6 * 5 = 210 ways correct option is b"
Answer: b
Python program:
a = 7 / 3
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 5 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 64 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 5 = 96 total boys : 160 - 96 = 64 answer is b"
Answer: b
Python program:
a = 160 / 5
b = a * 3
Problem: a train running at 7 / 11 of its own speed reached a place in 22 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 9 hrs , e ) 11 hrs
Rationale: "new speed = 7 / 11 of usual speed new time = 11 / 7 of usual time 11 / 7 of usual time = 22 hrs usual time = 22 * 7 / 11 = 14 hrs time saved = 22 - 44 = 8 hrs answer is c"
Answer: c
Python program:
a = 7 / 11
b = a * 22
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3300 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1980 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 132 so , a ’ s amount = 120 × 15 = rs . 1980 . answer : option c"
Answer: c
Python program:
a = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f 
h = b / g
i = h * 3300
Problem: a line that passes through ( – 2 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 2 ) = > 5 k = k + 4 = > k = 1 ans b it is !"
Answer: b
Python program:
a = 4 / 3
Problem: a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 23 : 120 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.33 m = = > revenue = price x quantity = 0.36 ( m + w ) = = > profit = 0.36 ( m + w ) - 0.33 m = 0.3 * ( 0.33 m ) [ 30 % of cost ] = = > 0.36 m + 0.36 w - 0.33 m = 0.099 m = = > 0.069 m = 0.36 w = = > m / w = 0.36 / 0.069 = 120 / 23 - - or - - w / m = 23 / 120 b is correct ."
Answer: b
Python program:
a = 30 / 2
b = 1 / a
Problem: carol is 5 times alice ’ s age but only twice as old as betty . alice is 12 years younger than carol . how old is betty ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24
Rationale: given that c = 5 a = 2 b . . and a = c - 12 = 5 a - 12 - - > 4 a = 12 - - > a = 3 substituting the values a = 3 , c = 15 and b = 6 . . ans a = 6 . .
Answer: a
Python program:
a = 5 + 1
Problem: a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has twice the width , twice the depth , and the same length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 15 , b ) 30 , c ) 20 , d ) 18 , e ) 25
Rationale: "volume of cube = lbh = 5 new cube l , b , h are increases of l , 2 b , 2 h new volume of cube = l * 2 b * 2 h = 4 * lbh = 4 * 5 = 20 answer : c"
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 5
Problem: in a box of 10 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 7 / 12 , b ) 11 / 20 , c ) 17 / 30 , d ) 28 / 45 , e ) 51 / 90
Rationale: "# defective pens = 2 # good pens = 8 probability of the 1 st pen being good = 8 / 10 probability of the 2 nd pen being good = 7 / 9 total probability = 8 / 10 * 7 / 9 = 28 / 45 the answer is d ."
Answer: d
Python program:
a = 10 - 2
b = a / 10
c = 10 - 2
d = c - 1
e = 10 - 1
f = d / e
g = b * f
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 30 , what is the sum of the first 15 terms of the progression ?
Options: a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230
Rationale: 4 th term + 12 th term = 30 i . e . , ( a + 3 d ) + ( a + 11 d ) = 30 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 30 - - - - - - - - - - - - - - - from ( 1 ) = 225 answer : d
Answer: d
Python program:
a = 15 / 2
b = a * 30
Problem: if x and y are numbers such that ( x + 5 ) ( y - 5 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16
Rationale: "from ( x + 5 ) ( y - 5 ) = 0 it follows that either x = - 5 or y = 5 . thus either x ^ 2 = 25 or y ^ 2 = 25 . now , if x ^ 2 = 8125 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 25 + 0 = 25 . similarly if y ^ 2 = 25 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 25 = 25 . answer : d ."
Answer: d
Python program:
a = 5 ** 2
Problem: find the value of ( 19 + 43 / 151 ) × 151
Options: a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215
Rationale: "= ( 19 + 43 / 151 ) × 151 = ( 2869 + 43 ) / 151 × 151 = 2912 / 151 × 151 = 2912 answer is d ."
Answer: d
Python program:
a = 43 / 151
b = a + 19 
c = b * 151
Problem: the lcm of two numbers is 2310 and hcf is 61 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 671 , c ) 330 , d ) 582 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 61 / 210 = 11 * 61 = 671 answer : b"
Answer: b
Python program:
a = 2310 * 61
b = a / 210
Problem: the c . p of 30 books is equal to the s . p of 40 books . find his gain % or loss % ?
Options: a ) 23 % , b ) 24 % , c ) 25 % , d ) 50 % , e ) 40 %
Rationale: "explanation : 30 cp = 40 sp 40 - - - 10 cp loss 100 - - - ? = > 25 % loss answer : c"
Answer: c
Python program:
a = 30 / 40
b = 1 - a
c = b * 100
Problem: a train 280 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 15 , b ) 6 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 280 * 3 / 55 = 15 sec . answer : a"
Answer: a
Python program:
a = 60 + 6 
b = a * const_0_2778
c = 280 / b
Problem: a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 30 paise per sq m is
Options: a ) rs . 223.20 , b ) rs . 323.20 , c ) rs . 423.20 , d ) rs . 523.20 , e ) none of these
Rationale: "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 30 / 100 ) = rs . 223.20 answer : a"
Answer: a
Python program:
a = 30 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f 
h = b + g 
i = a * h
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 5 men and 2 women will do that task .
Options: a ) 6 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 5 m + 2 w = 12 w answer is 12 / 14 = 6 / 7 answer : a"
Answer: a
Python program:
a = 8 - 2
b = 6 - 3
c = a / b
d = c * 5
e = d + 2 
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2 
k = e / j
Problem: a sum of money at simple interest amounts to rs . 824 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 500 , b ) 698 , c ) 780 , d ) 910 , e ) 725
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 824 ) = rs . 30 . s . i . for 3 years = rs . ( 30 * 3 ) = rs . 90 . â ˆ ´ principal = rs . ( 815 - 90 ) = rs . 725 answer e"
Answer: e
Python program:
a = 854 - 824
b = a * 3
c = b / 4
d = 824 - c
Problem: 6 boysand 8 girls can do job in 10 days , 26 boys & 48 women do work in 2 days find time taken by 15 boys and 20 girls to do same work
Options: a ) 4 days , b ) 5 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: 6 b + 8 g = 1 / 10 ( 1 day work ) - - - - - - > ( i ) 26 b + 48 w = 1 / 2 - - - - - - - - > ( ii ) divide both sides by 2 in ( i ) and multiply both sides by 5 now we get 15 b + 20 b = 1 / 4 so ans . is 4 days . answer : a
Answer: a
Python program:
a = 48 * 2
b = 8 * 10
c = a - b
d = 6 * 10
e = 26 * 2
f = d - e
g = c / f
h = g * 2
Problem: a , b and c have rs . 250 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 300 , b ) b ) 290 , c ) c ) 280 , d ) d ) 270 , e ) e ) 66
Rationale: "a + b + c = 250 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 250 - - - - - - - - - - - - - - - - c = 300 answer : a"
Answer: a
Python program:
a = 200 + 350 
b = a - 250
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1947 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 62 , d ) 122 , e ) 118
Rationale: "factorise 1947 . . 3 * 11 * 59 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 59 = 118 . . ans : e"
Answer: e
Python program:
a = 10 + 1 
b = 1947 / a
c = b / 3
d = 2 * c
Problem: a boat can travel with a speed of 14 km / hr in still water . if the speed of the stream is 6 km / hr , find the time taken by the boat to go 72 km downstream .
Options: a ) 4.25 hr , b ) 3.6 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 14 km / hr speed of the stream = 6 km / hr speed downstream = ( 14 + 6 ) = 20 km / hr time taken to travel 72 km downstream = 72 â  „ 20 = 3.6 hours answer is b"
Answer: b
Python program:
a = 14 + 6 
b = 72 / a
Problem: if x is equal to the sum of the integers from 40 to 60 , inclusive , and y is the number of even integers from 40 to 60 , inclusive , what is the value of x + y ?
Options: a ) 1021 , b ) 1041 , c ) 1061 , d ) 1081 , e ) 1101
Rationale: "x = 40 + 41 + . . . + 60 = 21 ( 50 ) = 1050 y = 11 x + y = 1061 the answer is c ."
Answer: c
Python program:
a = 40 + 60 
b = a / 2
c = 60 - 40
d = c + 1 
e = b * d
f = 60 - 40
g = f / 2
h = g + 1 
i = e + h
Problem: the average age of 36 students in a group is 15 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 35 years , b ) 45 years , c ) 52 years , d ) 54 years , e ) none of these
Rationale: "explanation : age of the teacher = ( 37 * 16 - 36 * 15 ) years = 52 years . answer : c"
Answer: c
Python program:
a = 36 + 1
Problem: how many paying stones , each measuring 4 m * 2 m are required to pave a rectangular court yard 40 m long and 20 m board ?
Options: a ) 99 , b ) 18 , c ) 100 , d ) 17 , e ) 12
Rationale: "40 * 20 = 4 * 2 * x = > x = 100 answer : c"
Answer: c
Python program:
a = rectangle_area / (
Problem: convert the 12 / 36 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.5 kmph . , e ) 1.9 kmph .
Rationale: "15 / 36 m / s = 12 / 36 * 18 / 5 = 1 ( 1 / 5 ) = 1.2 kmph . answer : c"
Answer: c
Python program:
a = 12 / 36
b = const_3_6 * a
Problem: a two digit number is 18 less than the sum of the squares of its digits . how many such numbers are there ?
Options: a ) 22 , b ) 67 , c ) 200 , d ) 288 , e ) 111
Rationale: "option 2 only 47 and 67 satisfy the condition answer : b"
Answer: b
Python program:
a = 100 / 2
b = a * 10
c = 18 ** 3
d = b + c
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 4 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 3 / 4 , b ) 9 / 16 , c ) 16 / 3 , d ) 4 / 3 , e ) 3 / 16
Rationale: "the area of rectangle a is ab . c = 4 a / 3 and d = 4 b / 3 . the area of rectangle b is cd = 16 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 16 ab / 9 ) = 9 / 16 . the answer is b ."
Answer: b
Python program:
a = 3 ** 2
b = 4 ** 2
c = a / b
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7 / 10 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 35.71429 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 7 x / 10 hence , number of buckets needed = 25 x / ( 7 x / 10 ) = ( 25 × 10 ) / 7 = 35.71429 answer is d ."
Answer: d
Python program:
a = 4 + 1 
b = 25 * a
c = b / 2
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 46 kg , then the weight of b is :
Options: a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 37 kg
Rationale: "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 46 = 92 hence 80 + 92 - 144 = 37 ans = 37 answer : e"
Answer: e
Python program:
a = 40 * 2
b = 46 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 2 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 9 : 5
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 4 and 2 parts , respectively . this will give us in the final mixture ( 5 + 4 ) : ( 3 + 2 ) , which means 9 : 5 answer e ."
Answer: e
Python program:
a = 4 * 5
b = 5 + 3 
c = b / 2
d = 3 * c
e = a + d 
f = 4 * 3
g = 5 + 3 
h = g / 2
i = 3 * h
j = f + i 
k = e / j
Problem: in covering a distance of 30 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "abhay speed = x sameer speed = y ( 30 / x ) - ( 30 / y ) = 2 . . . . 1 - ( 30 / 2 x ) + ( 30 / y ) = 1 . . . - 2 solving 1 and 2 we get 6 x = 30 x = 5 answer e"
Answer: e
Python program:
a = 30 / 2
b = 30 - a
c = 1 + 2 
d = b / c
Problem: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.05 ?
Options: a ) 980 , b ) 1130 , c ) 1440 , d ) 1610 , e ) 1820
Rationale: the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.05 - $ 0.65 = $ 1.40 the charge for the next 1300 grams is $ 1.30 which leaves a charge of $ 0.10 the weight is somewhere between 1550 and 1650 . the answer is d .
Answer: d
Python program:
a = 65 / 100
b = 2 - 5
c = 10 / 100
d = c / 100
e = d * 250
f = b + e 
g = 10 / 100
h = g / 100
i = f / h
Problem: the area of a square garden is a square feet and the perimeter is p feet . if a = 2 p + 14.25 , what is the perimeter of the garden , in feet ?
Options: a ) 38
b ) 36
c ) 40
d ) 56
e ) 64
Rationale: perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 14.25 ( p ^ 2 ) / 16 = 2 p + 9 p ^ 2 = 32 p + 228 p ^ 2 - 32 p - 228 = 0 p ^ 2 - 38 p + 6 p - 228 = 0 p ( p - 38 ) + 6 ( p + 38 ) = 0 ( p - 38 ) ( p + 6 ) = 0 p = 38 or - 6 discarding negative value , p = 38 answer is a
Answer: a
Python program:
a = 14 * 25
b = 10 + a 
c = b - const_0_25
d = c - const_0_25
Problem: a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 1 / 2 % his yearly income diminishes by rs . 61.50 . his capital is
Options: a ) 223.78 , b ) 37.78 , c ) 24.6 , d ) 278.88 , e ) 123.0
Rationale: "explanation : capital = rs . x , then 1 / 2 x = 61.5 x = 123.00 answer : e ) rs . 123.00"
Answer: e
Python program:
a = 4 / 2
b = 61 / 50
Problem: a fruit seller had some oranges . he sells 20 % oranges and still has 380 oranges . how many oranges he had originally ?
Options: a ) 475 , b ) 700 , c ) 220 , d ) 400 , e ) none of these
Rationale: explanation : he sells 20 % of oranges and still there are 380 oranges remaining = > 80 % of oranges = 380 ⇒ ( 80 × total oranges ) / 100 = 380 ⇒ total oranges / 100 = 4.75 ⇒ total oranges = 4.75 × 100 = 475 answer : option a
Answer: a
Python program:
a = 20 / 100
b = 380 * a
c = 380 + b
Problem: find the mean proportional between 25 & 36 ?
Options: a ) a ) 59 , b ) b ) 30 , c ) c ) 63 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 25 and b = 36 √ 25 × 36 = 5 × 6 = 30 b"
Answer: b
Python program:
a = 25 + 36 
b = a / 2
Problem: the compound ratio of 2 / 5 , 6 / 7 , 1 / 3 and 1 / 8 is given by ?
Options: a ) 7 / 98 , b ) 1 / 70 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 5 * 6 / 7 * 1 / 3 * 1 / 8 = 12 / 840 = 1 / 70 answer : b"
Answer: b
Python program:
a = 2 * 7
b = 1/(a)
Problem: p , q and r can do a work in 5 , 7 and 10 days respectively . they completed the work and got rs . 310 . what is the share of q and r respectively ?
Options: a ) 100 and 80 , b ) 100 and 90 , c ) 100 and 110 , d ) 70 and 100 , e ) 100 and 70
Rationale: the ratio of their working rates = 1 / 5 : 1 / 7 : 1 / 10 = 14 : 10 : 7 . since , they work together , the share of q = 10 / 31 * 310 = rs . 100 the share of r = 7 / 31 * 310 = rs . 70 the share of q and r respectively is rs . 100 and rs . 70 answer : e
Answer: e
Python program:
a = 100 * 100
b = 310 * 7
c = 7 * 10
d = c / 5
e = d + 7 
f = e + 10 
g = b / f
h = a + g
Problem: what is the average ( arithmetic mean ) of the numbers 16 , 17 , 18 , 19 and 20 ?
Options: a ) 14.2 , b ) 16.5 , c ) 17 , d ) 17.5 , e ) 18
Rationale: "{ 16 , 17 , 18 , 19 , 20 } = { 18 - 2,18 - 1 , 18 , 18 + 1,18 + 2 } - - > the average = 18 . answer : e ."
Answer: e
Python program:
a = 16 + 18 
b = 18 - 16
c = b / 16
d = c + 1 
e = a * d
f = e / 2
g = 18 - 16
h = g / 16
i = h + 1 
j = f / i
Problem: a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 267 , d ) 261 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 841 = 261 answer : d"
Answer: d
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 841 / e
g = 16 * 9
h = f * g