euclaise/mathqa_programs huggingface dataset:
Problem: i sold a book at a profit of 10 % . had i sold it for $ 100 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 100 5 % of cost = $ 100 cost = 100 * 100 / 5 = $ 2000 answer is a"
Answer: a
Python program:
a = 100 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
Problem: an inspector rejects 0.08 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) 1200 , b ) 1240 , c ) 1852 , d ) 3200 , e ) 2500
Rationale: "then , 0.08 % of x = 2 ( 8 / 100 ) * ( 1 / 100 ) x = 2 x = ( 2 * 100 * 100 ) / 8 = 2500 answer is e"
Answer: e
Python program:
a = 2 * 100
b = a / 0
Problem: the average age of a class is 15.8 years . the average age of the boys in the class is 16.4 years and that of the girls is 15.4 years . what is the ratio of boys to girls in the class ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: "let number of boys = x ; let number of girls = y total numbers of students = x + y ( x + y ) × 15.8 = 16.4 x + 15.4 y 0.6 x = 0.4 y x / y = 0.4 / 0.6 = 2 / 3 answer : c"
Answer: c
Python program:
a = 15 - 8
b = 16 - 4
c = a / b
Problem: in how many years will a sum of money doubles itself at 25 % per annum on simple interest ?
Options: a ) 4 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "p = ( p * 25 * r ) / 100 r = 4 % answer : a"
Answer: a
Python program:
a = 100 / 25
Problem: log 3 n + log 7 n what is 3 digit number n that will be whole number
Options: a ) 343 , b ) 729 , c ) 829 , d ) 929 , e ) 727
Rationale: no of values n can take is 1 7 ^ 3 = 343 answer : a
Answer: a
Python program:
a = 7 ** 3
Problem: at the a - street fish market a vendor sells fresh caught fish . his store is filled with 2 / 7 bass , 1 / 5 tuna , 1 / 7 trout , and the rest are catfish . if a customer just bought 1 / 7 of all the tuna and 1 / 7 of all the catfish , and a fisherman arrived to restock the bass , doubling the number of bass , what proportion of fish now in the store are trout ?
Options: a ) 30 / 71 , b ) 4 / 7 , c ) 5 / 43 , d ) 1 / 2 , e ) 1 / 5
Rationale: bass = 2 / 7 = 10 / 35 tuna = 1 / 5 = 7 / 35 trout = 1 / 7 = 5 / 35 catfish = 1 - ( 10 / 35 + 7 / 35 + 5 / 35 ) = 13 / 35 purchased : tuna = 7 / 35 - ( 7 / 35 ) ( 1 / 7 ) = 6 / 35 , and catfish = 13 / 35 - ( 13 / 35 ) ( 1 / 7 ) = 12 / 35 stocked : doubling the number of bass ( 2 ) ( 10 / 35 ) = 20 / 35 now : 20 + 6 + 5 + 12 = 43 trout proportion is now 5 / 43 . answer : c
Answer: c
Python program:
a = 1 / 5
b = 2 / 7
c = 1 / 5
d = b + c 
e = 1 / 7
f = d + e 
g = 1 - f
h = 2 / 7
i = g - h
j = a - i
Problem: a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . whatwill be b ' s share in total profit of rs . 20000 earned at the end of 2 years from the startingof the business ?
Options: a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500
Rationale: a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d
Answer: d
Python program:
a = 12 * 2
b = 15000 * a
c = 12 * 2
d = 20000 * c
e = 12 * 2
f = 15000 * e
g = d + f 
h = 12 * 2
i = h - 6
j = i * 20000
k = g + j 
l = b / k
m = 20000 * l
n = m / 12
Problem: the product of two positive integers is 323 and their difference is 2 . what is the smaller number ?
Options: a ) 17 , b ) 18 , c ) 16 , d ) 19 , e ) 14
Rationale: let ' s use trial and error to find the two numbers . 20 * 18 = 360 ( too high ) 19 * 17 = 323 the answer is a .
Answer: a
Python program:
a = 323 / 2
b = 323 / a
c = b * 4
d = c + 10 
e = d - 1
Problem: an alloy is to contain steel and iron in the ratio 5 : 2 . the iron required to be melted with 35 kg of steel is ?
Options: a ) 12 kg , b ) 14 kg , c ) 15 kg , d ) 20 kg , e ) 18 kg
Rationale: let the required quantity of steel be x kg 5 : 2 : : 35 : x 5 x = 2 * 35 x = 14 kg answer is b
Answer: b
Python program:
a = 35 / 5
b = a * 2
Problem: a man complete a journey in 30 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 10 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 400 km , e ) 234 km
Rationale: 0.5 x / 20 + 0.5 x / 10 = 30 - - > x / 20 + x / 10 = 60 - - > 3 x = 20 x 60 - - > x = ( 60 x 20 ) / 3 = 400 km . answer : d
Answer: d
Python program:
a = 20 * 10
b = a * 30
c = 20 + 10 
d = b / c
e = 2 * d
Problem: a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 52 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 60 ) kmph = 52 kmph . answer : a"
Answer: a
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 60
Problem: 0.0006 ? = 0.03
Options: a ) 2 , b ) 20 , c ) 0.2 , d ) 0.02 , e ) none of these
Rationale: "explanation : required answer = 0.0006 / 0.03 = 0.06 / 3 = 0.02 . answer : option d"
Answer: d
Python program:
a = 0 / 6
b = a * 100
Problem: a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 49 , c ) 88 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : b"
Answer: b
Python program:
a = 4 * const_0_2778
b = a * 4
c = 125 - b
d = c / 10
e = d / const_0_2778
Problem: it would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order . how many hours would it take both machines , working simultaneously at their respective constant rates , to complete the order ?
Options: a ) 72 / 17 , b ) 17 / 72 , c ) 14 / 24 , d ) 24 / 56 , e ) 34 / 56
Rationale: the rate of the first machine is 1 / 9 job per hour ; the rate of the second machine is 1 / 8 job per hour ; thus , the combined rate of the machines is 1 / 9 + 1 / 8 = 17 / 72 job per hour , which means that it takes 1 / ( 17 / 72 ) = 72 / 17 hours both machines to do the job . answer : a .
Answer: a
Python program:
a = 9 * 8
b = 9 + 8 
c = a / b
Problem: 3034 − ( 1002 ÷ 20.04 ) = ?
Options: a ) 1964 , b ) 1984 , c ) 2964 , d ) 2984 , e ) none of these
Rationale: "explanation : = 3034 − ( 1002 / 2004 × 100 ) = 3034 − 50 = 2984 option d"
Answer: d
Python program:
a = 1002 / 20
b = 3034 - a
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 57 . what is that number ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 57 2 x = 10 = > x = 5 answer : a"
Answer: a
Python program:
a = 3 * 9
b = 57 - a
c = 3 * 2
d = b / c
Problem: a room is 5 meters 76 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 5 meters and 76 centimeters = 576 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 576 and 432 = 144 thus , the number of square tiles required = ( 576 x 432 ) / ( 144 x 144 ) = 4 x 3 = 12 answer : b"
Answer: b
Python program:
a = 5 * 100
b = a + 76 
c = 4 * 100
d = c + 32 
e = b * d
f = 5 * 100
g = f + 76 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 5 * 100
l = k + 76 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p
Problem: a train sets off at 2 : 00 pm at the speed of 70 km / h . another train starts at 3 : 00 pm in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ?
Options: a ) 10 : 00 , b ) 10 : 30 , c ) 11 : 00 , d ) 11 : 30 , e ) 12 : 00
Rationale: in one hour the first train travels 70 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 70 / 10 = 7 hours , so at 10 : 00 pm . the answer is a .
Answer: a
Python program:
a = 80 - 70
b = 70 / a
c = b + 3
Problem: a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 3 hours 24 minutes , e ) none
Rationale: "solution speed downstream = ( 15 + 5 ) km / hr = 20 km / hr . time taken to travel 68 km downstream = ( 68 / 20 ) hrs = 3 hrs 24 minutes . answer d"
Answer: d
Python program:
a = 15 + 5 
b = 68 / a
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 9 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "if n = 10 mark sold 1 box and ann sold 8 boxes total 9 < 10 answer : b"
Answer: b
Python program:
a = 9 + 1
Problem: 135 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 54 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 135 = 81 liters water = 54 liters 81 : ( 54 + p ) = 3 : 4 162 + 3 p = 324 = > p = 54 54 liters of water are to be added for the ratio become 3 : 4 . answer : d"
Answer: d
Python program:
a = 3 + 2 
b = 135 / a
c = b * 2
Problem: 17 times a positive integer is more than its square by 60 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 5 , e ) 14
Rationale: "explanation : let the number be x . then , 17 x = x 2 + 60 = > x 2 - 17 x + 60 = 0 = > ( x - 12 ) ( x - 5 ) = 0 = > x = 5 or 12 answer : option d"
Answer: d
Python program:
a = 17 ** 2
b = 60 * 4
c = a - b
d = 17 + c 
e = d / 2
Problem: a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ?
Options: a ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15
Rationale: "let ' s see pick 40 / 1000 first then we can only pick 1 other pair from the 800 so total will be 40 / 800 * 1000 simplify and you get 1 / 20000 answer is c"
Answer: c
Python program:
a = 1 / 3
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer is c"
Answer: c
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 480 square feet . how many feet offence does frank use ?
Options: a ) 14
b ) 47
c ) 54
d ) 180
e ) 64
Rationale: area = length x breadth 480 = 40 x breadth so , breadth = 12 units fencing required is - breadth + breadth + length 12 + 12 + 40 = > 64 feet answer must be ( e ) 64
Answer: e
Python program:
a = 480 / 40
b = 480 / 40
c = a + b 
d = c + 40
Problem: the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 6804 cu . m . its width is
Options: a ) 3 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
Rationale: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 6804 x = 3 answer : a"
Answer: a
Python program:
a = 6 * 7
b = a * 6
c = 6804 / b
d = 1 / 3
e = c ** d
Problem: 90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 35 , c ) 42 , d ) 27 , e ) 11
Rationale: x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 90 = 35 answer : b
Answer: b
Python program:
a = 4 + 3 
b = 4 + 3 
c = b + 2 
d = a / c
e = d * 90
f = e / 2
Problem: a train running at 1 / 3 of its own speed reached a place in 9 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 3 * 9 = 3 hrs time saved = 9 - 3 = 6 hrs answer : e"
Answer: e
Python program:
a = 1 / 3
b = a * 9
Problem: the radius of a semi circle is 7 cm then its perimeter is ?
Options: a ) 32.8 , b ) 36 , c ) 32.1 , d ) 32.2 , e ) 32.9
Rationale: "radius = 7 cm then diameter = 14 cm 1 / 2 * 22 / 7 * 14 + 14 = 36 answer : b"
Answer: b
Python program:
a = circumface / (
b = a + 2
Problem: two persons raj and ramu started working for a company in similar jobs on january 1 , 1991 . raj ' s initial monthly salary was rs 400 , which increases by rs 40 after every year . ramu ' s initial monthly salary was rs 500 which increases by rs 20 after every 6 months . if these arrangements continue till december 31 , 200 . find the total salary they received during that period .
Options: a ) rs 108000 , b ) rs 144000 , c ) rs 132000 , d ) rs 152400 , e ) none of these
Rationale: explanation : raj ' s salary as on 1 jan 1991 is rs 400 per month . his increment in his month salary is rs 40 per annum his total salary from 1 jan 1991 to 31 st dec 2000 i . e . in ten years = > 12 [ 2 ( 400 ) + ( 10 − 1 ) 40 ] × 10 / 2 . = > rs 69600 . ramu ' s salary as on jan 1 st 1991 is rs 550 and his half yearly increment in his month salary is rs 20 . his total salary from 1 jan 1991 to dec 31 , 2000 = > 6 [ 2 ( 500 ) + ( 20 − 1 ) 20 ] × 20 / 2 . = > rs 82000 . total salary of raj and ramu in the ten year period : = > rs . 69600 + rs . 82800 . = > rs 1 , 52400 . answer : d
Answer: d
Python program:
a = 2 * 400
b = 10 - 1
c = 40 * b
d = a + c 
e = d * 12
f = 2 + 3 
g = e * f
h = 2 * 500
i = 20 - 1
j = i * 20
k = h + j 
l = k * 6
m = l * 10
n = g + m
Problem: at a certain college , 80 percent of the total number of students are freshmen . if 60 percent of the fresh - men are enrolled in the school of liberal arts and , of these , 50 percent are psychology majors , what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ?
Options: a ) 25 % , b ) 20 % , c ) 22 % , d ) 21 % , e ) 24 %
Rationale: let ' s say there is a total of 100 students at this college . 80 percent of the total number of students are freshmen . # of freshmen = 80 % of 100 = 80 60 percent of the fresh - men are enrolled in the school of liberal arts . . . number of liberal arts freshmen = 60 % of 80 = 48 . . . and , of these , 50 percent are psychology majors . . . number of liberal arts freshmen who are psychology majors = 50 % of 48 = 24 what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts ? 24 / 100 = 24 % answer : e
Answer: e
Python program:
a = 80 * 60
b = a / 100
c = b * 50
d = c / 100
Problem: difference of two numbers is 1670 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2490 , 4150 , e ) 2505 , 4175
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1670 5 * y / 3 – y = 1670 2 * y / 3 = 1670 y = [ ( 1670 * 3 ) / 2 ] = 2505 . one number = 2505 , second number = 5 * y / 3 = 4175 . answer e ."
Answer: e
Python program:
a = 7 / 5
b = 7 / 5
c = 1 - b
d = 1670 / c
e = a * d
Problem: the ratio of flour to water to sugar in a recipe is 11 : 8 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 4 cups of water , how much sugar is required ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "the ratio of flour to water is 22 : 8 = 11 : 4 . the ratio of flour to sugar is 5.5 : 1 = 11 : 2 . the new ratio of flour to water to sugar is 11 : 4 : 2 if we need 4 cups of water , then we need 2 cups of sugar . the answer is d ."
Answer: d
Python program:
a = 4 / 8
b = 4 * 1
c = a * b
Problem: craig sells major appliances . for each appliance he sells , craig receives a commission of $ 50 plus 10 percent of the selling price . during one particular week craig sold 6 appliances for selling prices totaling $ 3620 . what was the total of craig ' s commissions for that week ?
Options: a ) $ 412 , b ) $ 526 , c ) $ 585 , d ) $ 605 , e ) $ 662
Rationale: craig receives a commission of $ 50 on each appliance plus a 10 % commission on total sales , thus his commission was 6 * 50 + 0.1 * 3620 = 662 . answer : e .
Answer: e
Python program:
a = 3620 / 10
b = 50 * 6
c = a + b
Problem: if 8 ^ x = 2 ^ 9 , what is x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 2 ^ 3 x = 2 ^ 9 3 x = 9 , therefore x = 3 answer b
Answer: b
Python program:
a = 9 / 3
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 3 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 3 / 23
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 3 * x hence , a 1 + a 2 + . . + a 20 + n = 23 x so , the fraction asked = 3 x / 23 x = 3 / 23 answer e"
Answer: e
Python program:
a = 1 * 1
b = 20 / 3
c = b + 21 
d = c / 4
e = d * 2
f = e - 3
g = f - 3
h = a / g
Problem: i chose a number and divide it by 8 . then i subtracted 100 from the result and got 6 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 848
Rationale: "solution : let x be the number i chose , then x / 8 â ˆ ’ 100 = 6 x / 8 = 106 x = 848 answer e"
Answer: e
Python program:
a = 100 + 6 
b = a * 8
Problem: the population of a bacteria colony doubles every day . if it was started 7 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 128 , b ) 256 , c ) 512 , d ) 1024 , e ) 2048
Rationale: 2 ^ 7 ( 2 ) = 2 ^ 8 = 256 the answer is b .
Answer: b
Python program:
a = 7 + 1 
b = 2 ** a
c = b - 1
Problem: light glows for every 32 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 180 times , b ) 381 times , c ) 155 times , d ) 392 times , e ) 150 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 32 ) = 15582 times . answer : c"
Answer: c
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 32
Problem: if the height of a right cone c is 3 and the diameter of the base of c is 8 , what is the distance from the apex of c to any point on the circumference of the base of c ?
Options: a ) 3 √ 2
b ) 5
c ) 5 √ 2
d ) √ ( 67 )
e ) √ ( 73 )
Rationale: height of cone = 3 radius of base = 4 so the distance from the apex of c to any point on the circumference of the base of c will be a right angled triangle hence the distance is sqrt ( 3 ^ 2 + 4 ^ 2 ) = 5 answer : b
Answer: b
Python program:
a = 8 / 2
b = a ** 2
c = 3 ** 2
d = b + c 
e = math.sqrt(d)
Problem: a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . how many hours are required for b to copy 26 papers ?
Options: a ) 11 hours , b ) 12 hours , c ) 13 hours , d ) 14 hours , e ) 18 hours
Rationale: a can copy 50 papers in 10 hrs , while a & b can copy 70 papers in 10 hrs . it means b can copy 20 papers in 10 hrs . then time taken by b to copy 26 papers = 26 * 10 / 20 = 13 hours answer : c
Answer: c
Python program:
a = 26 * 10
b = 70 - 50
c = a / b
Problem: 45 % of 816 - 23 % of ? = 240.7
Options: a ) 330 , b ) 440 , c ) 240 , d ) 550 , e ) 230
Rationale: "d 550 ( 816 * 45 ) / 100 - ( ? * 23 ) / 100 = 240.7 = > 367.2 - ( ? * 23 ) / 100 = 240.7 = > ( ? * 23 ) / 100 = 367.2 - 240.7 = > ? = ( 126.5 * 100 ) / 23 = 550"
Answer: d
Python program:
a = 45 * 816
b = a / 23
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 121 hours and 100 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 100 : â ˆ š 121 = 10 : 11 . answer e"
Answer: e
Python program:
a = math.sqrt(100)
b = math.sqrt(121)
c = a / b
Problem: shanmukham buys good worth rs . 6650 . he gets a rebate of 6 % on it . after getting the rebate , he pays sales tax @ 10 % . find the amount he will have to pay for the goods
Options: a ) 6999.2 , b ) 6876.1 , c ) 6654 , d ) 7000 , e ) none of these
Rationale: explanation : rebate = 6 % of rs . 6650 = rs . 6 / 100 x 6650 = rs . 399 . sales tax = 10 % of rs . ( 6650 399 ) = rs . 10 / 100 x 6251 = rs . 625.10 final amount = rs . ( 6251 + 625.10 ) = rs . 6876.10 answer : b
Answer: b
Python program:
a = 6650 * 6
b = a / 100
c = 6650 - b
d = 6650 * 6
e = d / 100
f = 6650 - e
g = f * 10
h = g / 100
i = c + h
Problem: the maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 71 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 781 and 710 . â € ¹ = â € º 71 . answer a"
Answer: a
Python program:
a = 781 - 710
Problem: what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 27 units ?
Options: a ) 8.5 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 2 units
Rationale: "sides are 8 , 15 and 27 . . . thus it is right angle triangle since 27 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 27 + 15 + 8 / 2 = 30 thus , 60 = 30 * r and hence r = in - radius = 2 option e"
Answer: e
Python program:
a = triangle_area_three_edges / (
Problem: the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 3 years hence ?
Options: a ) 58 , b ) 59 , c ) 62 , d ) 66 , e ) 74
Rationale: explanation : a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 3 years , their ages will be 43 and 23 . sum of their ages = 43 + 23 = 66 . d )
Answer: d
Python program:
a = 60 / 3
b = a * 2
c = b + 3 
d = 60 / 3
e = d + 3 
f = c + e
Problem: two trains 120 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 11.6 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 20.8 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 190 = 310 m . required time = 310 * 9 / 250 = 11.6 = 11.6 sec . answer : b"
Answer: b
Python program:
a = 120 + 190 
b = 60 + 40 
c = b * const_0_2778
d = a / c