euclaise/mathqa_programs huggingface dataset:
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 7 pencils and 11 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 7 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 18 so a + b = 6 total number of people = 6 a"
Answer: a
Python program:
a = 11 + 7 
b = 2 + 1 
c = a / b
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number r ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = r answer : b"
Answer: b
Python program:
a = 12 / 5
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b - d
f = 30 / e
Problem: the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 180.27 cm , b ) 180.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b"
Answer: b
Python program:
a = 35 * 182
b = a - 166
c = b + 106 
d = c / 35
e = math.floor(d)
Problem: the salaries of a and b together amount to $ 3000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 2250 , e ) $ 1200
Rationale: "let a ' s salary is x b ' s salary = 3000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 3000 - x ) x = $ 2250 answer is d"
Answer: d
Python program:
a = 100 - 85
b = 100 - 95
c = a / b
d = c + 1 
e = 3000 / d
f = 3000 - e
Problem: if a number is subtracted from its square we get 272 . find the number ?
Options: a ) 7
b ) 21
c ) 19
d ) 15
e ) 17
Rationale: x ^ 2 â € “ x = 272 = > x = 17 answer e
Answer: e
Python program:
a = 4 * 272
b = 1 + a 
c = math.sqrt(b)
d = 1 + c 
e = d / 2
Problem: a train 120 m long crosses a platform 220 m long in 20 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 54 kmph , d ) 61 kmph , e ) 18 kmph
Rationale: "d = 120 + 220 = 340 t = 20 s = 340 / 20 * 18 / 5 = 61 kmph answer : d"
Answer: d
Python program:
a = 220 * const_0_2778
b = 20 * a
c = b - 120
Problem: for all positive integers m and v , the expression m θ v represents the remainder when m is divided by v . what is the value of ( ( 88 θ 33 ) θ 17 ) - ( 90 θ ( 33 θ 17 ) ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( ( 88 θ 33 ) θ 17 ) the remainder of 88 divided by 33 is 22 ; the remainder of 22 divided by 17 is 5 ; ( 98 θ ( 33 θ 17 ) ) the remainder of 33 divided by 17 is 16 ; the remainder of 98 divided by 16 is 2 . 5 - 2 = 3 . answer : d ."
Answer: d
Python program:
a = reminder - (
Problem: if solomon distributes his toys in the ratio of 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 between his 4 friends a , b , c and d , then find the total number of toys solomon should have ?
Options: a ) 111.7 , b ) 118.7 , c ) 113.7 , d ) 218.7 , e ) 418.7
Rationale: here , a : b : c : d = 1 / 4 : 1 / 6 : 1 / 10 : 1 / 9 1 ) l . c . m of 4 : 6 : 10 : 9 is 180 2 ) find the number of pens each friend received - - - - - - - - - ( to find no . of pens each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 4 ) x 180 = 45 b = ( 1 / 6 ) x 180 = 30 c = ( 1 / 10 ) x 180 = 18 d = ( 1 / 7 ) x 180 = 25.7 3 ) total number of toys = ( 45 x + 30 x + 18 x + 25.7 x ) = 118.7 x minimum number of pens ( x ) = 1 therefore , total number of pens = 118.7 pens . correct option : b
Answer: b
Python program:
a = 10 * 6
b = 10 * 4
c = a + b 
d = 6 * 3
e = c + d
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.40 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.40 ) = rs . 5808 . answer : d ) 5808"
Answer: d
Python program:
a = 13 / 86
b = math.sqrt(a)
c = b * 100
d = circumface * (
Problem: an article is bought for rs . 675 and sold for rs . 1000 , find the gain percent ?
Options: a ) 34 % , b ) 44 % , c ) 48 % , d ) 32 % , e ) 46 %
Rationale: "675 - - - - 325 100 - - - - ? = > = 48 % answer : c"
Answer: c
Python program:
a = 1000 * 100
b = a / 675
c = 100 - b
Problem: a 13 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 92 , c ) rs . 162.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 13 , investment = rs . ( 100 / 8 x 13 ) = rs . 162.50 ∴ market value of rs . 100 stock = rs . 162.50 answer c"
Answer: c
Python program:
a = 100 / 8
b = a * 13
Problem: from a container , 6 liters milk was drawn out and was replaced by water . again 6 liters of mixture was drawn out and was replaced by the water . thus the quantity of milk and water in the container after these two operations is 9 : 16 . the quantity of mixture is :
Options: a ) 15 , b ) 26 , c ) 22 , d ) 27 , e ) 11
Rationale: explanation : let quantity of mixture be x liters . suppose a container contains x units of liquid from which y units are taken out and replaced by water . after operations , the quantity of pure liquid = units , where n = no of operations . so , quantity of milk = given that , milk : water = 9 : 16 milk : ( milk + water ) = 9 : ( 9 + 16 ) milk : mixture = 9 : 25 answer : a ) 15
Answer: a
Python program:
a = 9 + 16 
b = math.sqrt(a)
c = 6 * b
d = c / 2
Problem: a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 60 miles per hour and arrives in chicago at 5 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 10 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: 5 : 00 in evening in chicago = 6 : 00 in evening in new york . so , the train was in chicago 6 : 00 in the evening , new york time . the trip took t = d / r = 480 / 60 = 8 hours . therefore , the train depart from new york at 6 : 00 - 8 hours = 10 : 00 in the morning , new york time . answer : a .
Answer: a
Python program:
a = 5 + 1 
b = a * 3
c = 480 / 60
d = b - c
Problem: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 2 seconds ?
Options: a ) 4 , b ) 55 , c ) 15 , d ) 48 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 2 ) = 2 ^ 2 + 2 * 2 = 8 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 8 = 55 km / hr option b"
Answer: b
Python program:
a = 7 ** 2
b = 7 * 2
c = a + b 
d = 2 ** 2
e = 2 * 2
f = d + e 
g = c - f
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.6 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1990
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 1950 ro = 10 , ri = 40 1990 ro = 50 , ri = 80 = 1.6 times thus ans : e"
Answer: e
Python program:
a = 4 + 3 
b = 1 + 6 
c = 1950 + b
Problem: a room is 8 meters 16 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 ) 107 , b ) 153 , c ) 178 , d ) 198 , e ) 165
Rationale: "let us calculate both the length and width of the room in centimeters . length = 8 meters and 16 centimeters = 816 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 816 and 432 = 48 thus , the number of square tiles required = ( 816 x 432 ) / ( 48 x 48 ) = 17 x 9 = 153 answer : b"
Answer: b
Python program:
a = 8 * 100
b = a + 16 
c = 4 * 100
d = c + 32 
e = b * d
f = 8 * 100
g = f + 16 
h = 4 * 100
i = h + 32 
j = math.gcd(g, i)
k = 8 * 100
l = k + 16 
m = 4 * 100
n = m + 32 
o = math.gcd(l, n)
p = j * o
q = e / p
Problem: there are 8 executives , including the ceo and cfo , that are asked to form a small team of 5 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "the total number of ways to form a team of 5 is 8 c 5 = 56 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 6 c 3 = 20 . the number of ways to form an acceptable team is 56 - 20 = 36 . the answer is c ."
Answer: c
Python program:
a = 8 - 5
b = math.factorial(a)
c = 5 * 3
d = c + 3 
e = b - d
Problem: victor gets 92 % marks in examinations . if these are 460 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 288 , e ) 271
Rationale: "let the maximum marks be m then 92 % of m = 460 ⇒ 92 / 100 × m = 460 ⇒ m = ( 460 × 100 ) / 92 ⇒ m = 46000 / 92 ⇒ m = 500 therefore , maximum marks in the examinations are 500 . answer : b"
Answer: b
Python program:
a = 92 / 100
b = 460 / a
Problem: max planned to buy bike , sales man advised him to buy within this month , if he purchase next month means state tax will be increasing 10 % than its cost and it would be 82500 . what is the bike ' s selling price in this month
Options: a ) 70000 , b ) 73000 , c ) 75000 , d ) 77000 , e ) 79000
Rationale: sp * ( 110 / 100 ) = 82500 sp = 750 * 100 = > sp = 75000 answer : c
Answer: c
Python program:
a = 10 / 100
b = a + 1 
c = 82500 / b
Problem: a boy goes to his school from his house at a speed of 3 km / hr and returns at a speed of 2 km / hr . if he takes 5 hours in going and coming . the distance between his house and school is ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "average speed = ( 2 * 3 * 2 ) / ( 3 + 2 ) = 12 / 5 km / hr . distance traveled = 12 / 5 * 5 = 12 km . distance between house and school = 12 / 2 = 6 km . answer : c"
Answer: c
Python program:
a = 3 / 2
b = a + 1 
c = 5 / b
d = c * 3
Problem: in a 500 m race , ravi beats ramesh by 5 seconds or 100 m . they decide to run another race and this time ravi gives ramesh a head tart of 200 m . if ravi ’ s speed is twice his previous speed and ramesh ’ s speed is one and half times his previous speed , how far from the starting point should the winning post be so that they finish at the same time ?
Options: a ) 500 m , b ) 1000 m , c ) 1500 m , d ) 2000 m , e ) 2500 m
Rationale: ravi beats ramesh by 5 sec or 100 mtr . . . . means ramesh cover 100 mtr in 5 sec . . . . by this we can get ramesh speed in 20 m / sec 20 . . . . . . . . . . . . . in 1 sec 500 . . . . . . . . in 500 / 20 = 25 sec ( ramesh ' s time ) so ravi take 20 sec to cover 500 mtr . . . . . . by this we can get that ravis speed is 25 m / sec now assume x be the distance from staring line where we need to put the winning post . according to question ravi ’ s speed will be 25 * 2 = 50 m / sec & ramesh ’ s speed will be 20 * 1.5 = 30 m / sec now assume x be the distance from staring line where we need to put the winning post . they will take same time to reach the wining post . as ravi gives ramesh a 200 m ahead start so he has to accede x meter and ramesh has to accede ( x - 200 ) meter hence we may write , x / 50 = ( x - 200 ) / 30 x = 500 meter answer : a
Answer: a
Python program:
a = 500 * 1
Problem: a store owner estimates that the average price of type a products will increase by 25 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.25 * 4500 = 5625 cost of type b products next year = 1.1 * 8300 = 9130 total 5625 + 9130 = 14755 answer : a"
Answer: a
Python program:
a = 3 / 4
b = a * 1000
Problem: two isosceles triangles have equal vertical angles and their areas are in the ratio 25 : 49 . find the ratio of their corresponding heights .
Options: a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 2 / 3
Rationale: "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 25 / 49 - - > height / height = 5 / 7 . answer : d ."
Answer: d
Python program:
a = math.sqrt(25)
b = math.sqrt(49)
c = a / b
Problem: a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 280 , then how much amount should c pay as his share of rent ?
Options: a ) 35 , b ) 45 , c ) 25 , d ) 72 , e ) 55
Rationale: a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 280 × 9 / 35 = 8 × 9 = 72 answer is d
Answer: d
Python program:
a = 15 * 3
b = 10 * 7
c = 12 * 5
d = b + c 
e = 15 * 3
f = d + e 
g = a / f
h = 280 * g
Problem: exactly 30 % of the reporters for a certain wire service cover local politics in country x . if 25 % of the reporters who cover politics for the wire service do not cover local politics in country x , what percent of the reporters for the wire service do not cover politics ?
Options: a ) 20 % , b ) 42 % , c ) 60 % , d ) 80 % , e ) 84 %
Rationale: let ' s assume there are 100 reporters - - > 30 reporters cover local politics . now , as 25 % of the reporters who cover all politics do not cover local politics then the rest 75 % of the reporters who cover politics do cover local politics , so if there are x reporters who cover politics then 75 % of them equal to 30 ( # of reporters who cover local politics ) : 0.75 x = 30 - - > x = 40 , hence 40 reporters cover politics and the rest 100 - 40 = 60 reporters do not cover politics at all . answer : c .
Answer: c
Python program:
a = 100 - 25
b = 30 / a
c = 1 - b
d = c * 100
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 16 . what is the value of x ?
Options: a ) 20 , b ) 40 , c ) 80 , d ) 160 , e ) 320
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 16 ( y / 100 ) * x = 16 ( x / 400 ) * x = 16 x ^ 2 = 16 * 400 x = 80 the answer is c ."
Answer: c
Python program:
a = 50 / 16
b = 50 / 16
c = a * b
d = c * 1000
Problem: excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 16 , b ) 17 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 12 / 48 * 60 = 15 answer : c"
Answer: c
Python program:
a = 36 / 48
b = const_60 * a
c = const_60 - b
Problem: difference between the length & breadth of a rectangle is 26 m . if its perimeter is 208 m , then the ratio of area and perimeter is ? ? we have : ( l - b ) = 26 and 2 ( l + b ) = 208 or ( l + b ) = 104 ?
Options: a ) 315 : 26 , b ) 315 : 25 , c ) 315 : 30 , d ) 415 : 35 , e ) 425 : 35
Rationale: "solving the two equations , we get : l = 63 and b = 40 . area = ( l x b ) = ( 63 x 40 ) m 2 = 2520 m ^ 2 the required ratio is 2520 : 208 = 315 : 26 a"
Answer: a
Python program:
a = 3 / 2
Problem: everyone shakes hands with everyone else in a room . total number of handshakes is 105 . number of persons = ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 105 or n ( n - 1 ) = 210 or n = 15 answer is ( d )"
Answer: d
Python program:
a = 105 * 2
b = a / 3
c = b / 4
Problem: the price of a t . v . set worth rs . 12000 is to be paid in 20 installments of rs . 1200 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 29997 , b ) 10800 , c ) 27098 , d ) 19000 , e ) 2799
Rationale: money paid in cash = rs . 1200 balance payment = ( 12000 - 1200 ) = rs . 10800 . answer : b
Answer: b
Python program:
a = 12000 - 1200
Problem: two trains of length 140 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 28 , b ) 266 , c ) 990 , d ) 20 , e ) 21
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 140 + 280 = 420 m . the time required = d / s = 420 / 20 = 21 sec . answer : e"
Answer: e
Python program:
a = 140 + 280 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: the tax on a commodity is diminished by 28 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 19 % , c ) 32 % , d ) 12 % , e ) 52 %
Rationale: "100 * 100 = 10000 72 * 112 = 8064 10000 - - - - - - - 1936 100 - - - - - - - ? = 19.36 % answer : b"
Answer: b
Python program:
a = 100 + 12 
b = 100 - 28
c = a * b
d = c / 100
e = 100 - d
Problem: two mechanics were working on your car . one can complete the given job in 5 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 7 / 4 , b ) 4 / 3 , c ) 14 / 5 , d ) 10 / 3 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 5 rate ( 2 ) = 1 / 8 combined = 13 / 40 work done in 2 days = 13 / 20 work left = 7 / 20 rate * time = work left 1 / 8 * time = 7 / 20 time = 14 / 5 c"
Answer: c
Python program:
a = 4 + 2 
b = 1 / a
c = 1 / 5
d = b + c 
e = d * 2
f = 1 - e
g = 1 / 5
h = f / g
i = max(h)
Problem: how many multiples of 4 are there between 20 and 196 ?
Options: a ) 45 , b ) 42 , c ) 52 , d ) 43 , e ) 51
Rationale: "it should be mentioned whether 20 and 196 are inclusive . if 20 and 196 are inclusive , then the answer is ( 196 - 20 ) / 4 + 1 = 45 . if 20 and 196 are not inclusive , then the answer is ( 192 - 24 ) / 4 + 1 = 43 . since oa is d , then we have not inclusive case ."
Answer: d
Python program:
a = 196 - 20
b = a / 4
c = b + 1
Problem: a group of men decided to do a work in 6 days , but 4 of them became absent . if the rest of the group did the work in 12 days , find the original number of men ?
Options: a ) 15 , b ) 6 , c ) 40 , d ) 10 , e ) 8
Rationale: "original number of men = 4 * 12 / ( 12 - 6 ) = 8 answer is e"
Answer: e
Python program:
a = 4 * 12
b = 12 - 6
c = a / b
Problem: after 4 games , team b had an average of 61.5 points per game . if it got only 47 points in game 5 , how many more points does it need to score to get its total above 500 ?
Options: a ) 85 , b ) 74 , c ) 67 , d ) 53 , e ) 207
Rationale: "( 4 * 61.5 ) + 47 + x > 500 246 + 47 + x > 500 293 + x > 500 = > x > 207 option e"
Answer: e
Python program:
a = 4 * 61
b = a + 47 
c = 500 - b
Problem: the jogging track in a sports complex is 726 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 5.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 726 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 726 m apart , they take ( 100 / 825 * 726 / 1000 ) hrs = ( 242 / 2750 * 60 ) min = 5.28 min . answer : b"
Answer: b
Python program:
a = 726 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: two trains running in opposite directions cross a man standing on the platform in 35 seconds and 28 seconds respectively and they cross each other in 32 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 4 : 3 , c ) 3 : 8 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 35 x meters , and length of the second train = 28 y meters . ( 35 x + 28 y ) / ( x + y ) = 32 = = > 35 x + 28 y = 32 x + 32 y = = > 3 x = 4 y = = > x / y = 4 / 3 answer : option b"
Answer: b
Python program:
a = 35 - 32
b = 32 - 28
c = a / b
Problem: 40 % of a number is added to 120 , the result is the same number . find the number ?
Options: a ) 300 , b ) 277 , c ) 266 , d ) 200 , e ) 121
Rationale: ": ( 40 / 100 ) * x + 120 = x 2 x = 400 x = 200 answer : d"
Answer: d
Python program:
a = 120 / 100
b = 120 / a
Problem: 16.02 ã — 0.01 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.01 = 0.1602 the answer is a ."
Answer: a
Python program:
a = 16 / 2
b = a * 100
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2415 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 805 , d ) s . 900 , e ) s . 920
Rationale: 2415 * 1 / 3 = 805 option c
Answer: c
Python program:
a = 1 / 3
b = 2415 * a
Problem: 2 students appeared at an examination . 1 of them secured 9 marks more than the other one and hismarks was 56 % of the sum of their marks . find the marks obtained by them are ?
Options: a ) 39 and 31 , b ) 40 and 33 , c ) 42 and 33 , d ) 37 and 31 , e ) 35 and 32
Rationale: let their marks be ( x + 9 ) and x . then , x + 9 = 56 / 100 ( x + 9 + x ) = > 25 ( x + 9 ) = > 14 ( 2 x + 9 ) = > 3 x = 99 = > x = 33 . so , their marks are 42 and 33 c
Answer: c
Python program:
a = 9 * 100
b = 100 - 56
c = 56 - b
d = a / c
e = d * 56
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Python program:
a = 100 + 7 
b = 100 + 1 
c = a - b
d = 100 + 1 
e = 100 - 11
f = d - e
g = c / f
Problem: what is the hcf of 2 / 3 , 4 / 9 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 5 ) = 2 / 45 answer : option b"
Answer: b
Python program:
a = 2 / 5