euclaise/mathqa_programs huggingface dataset:
Problem: a train running at the speed of 54 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 135 , b ) 278 , c ) 255 , d ) 150 , e ) 287
Rationale: "speed = ( 54 * 5 / 18 ) m / sec = ( 15 ) m / sec length of the train = ( speed x time ) = ( 15 * 9 ) m = 135 m . answer : a"
Answer: a
Python program:
a = 54 * 1000
b = a / 3600
c = b * 9
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 44 kg , then the weight of b is :
Options: a ) 31 kg , b ) 32 kg , c ) 33 kg , d ) 34 kg , e ) none of these
Rationale: "explanation : let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 x 3 ) = 135 … . ( i ) a + b = ( 40 x 2 ) = 80 … . ( ii ) b + c = ( 44 x 2 ) = 88 … . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 168 … . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 33 . b ’ s weight = 33 kg . answer : c"
Answer: c
Python program:
a = 40 * 2
b = 44 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: the duplicate ratio of 3 : 4 is ?
Options: a ) 1 : 2 , b ) 1 : 4 , c ) 1 : 8 , d ) 9 : 16 , e ) 1 : 13
Rationale: "3 ^ 2 : 4 ^ 2 = 9 : 16 answer : d"
Answer: d
Python program:
a = 3 ** 2
b = 4 ** 2
c = a / b
Problem: in the first 15 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 35 overs to reach the target of 275 runs ?
Options: a ) 5.55 , b ) 6.25 , c ) 6.75 , d ) 7.02 , e ) 6.48
Rationale: required run rate = 275 - ( 3.2 x 15 ) / 35 = 227 / 35 = 6.48 option e
Answer: e
Python program:
a = 15 * 3
b = 275 - a
c = b / 35
Problem: a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 1800 in january , how many cars does he need to sell in february in order to double his january earnings ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: 1000 + 200 x = 3600 x = 13 cars . the answer is a .
Answer: a
Python program:
a = 1800 * 2
b = a - 1000
c = b / 200
Problem: the area of a sector of a circle of radius 4 cm formed by an arc of length 3.5 cm is ?
Options: a ) 7 , b ) 7.67 , c ) 8.75 , d ) 8.98 , e ) 8.28
Rationale: "( 4 * 3.5 ) / 2 = 7 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 4 * 3
c = a * b
Problem: working alone , a can complete a certain kind of job in 12 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "let total time taken by s to complete the job = s total time taken by a to complete the job = 12 work done by a in an hour 1 / a = 1 / 12 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / 12 = 1 / 4 - 1 / 12 = 1 / 6 = > d = 6 hours answer d"
Answer: d
Python program:
a = 1/(4)
b = 1/(12)
c = a - b
d = 1/(c)
Problem: a ’ s speed is 22 / 19 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 22 , b ) 1 / 19 , c ) 3 / 19 , d ) 2 / 19 , e ) 3 / 22
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 22 meters , b covers 19 meters in that time . so if the race is 22 meters long , when a reaches the finish line , b would be 3 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 3 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 22 meters ) would be the same as the time required by b ( to cover 19 meters ) to reach the finish line . so b should get a head start of 3 / 22 th of the race . answer ( e )"
Answer: e
Python program:
a = 22 - 19
b = a / 22
Problem: the average weight of 8 girls increases by 3 kg when a new girl comes in place of one of them weighing 70 kg . what might be the weight of the new girl ?
Options: a ) 94 kg , b ) 95 kg , c ) 96 kg , d ) 97 kg , e ) 98 kg
Rationale: total weight increased = 8 x 3 kg = 24 kg . weight of new person = 70 + 24 kg = 94 kg answer : a
Answer: a
Python program:
a = 8 * 3
b = a + 70
Problem: if t = 5 / 9 * ( k - 32 ) , and if t = 35 , then what is the value of k ?
Options: a ) 92 , b ) 95 , c ) 98 , d ) 101 , e ) 104
Rationale: "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 35 ) / 5 + 32 = 95 the answer is b ."
Answer: b
Python program:
a = 35 * 9
b = a / 5
c = b + 32
Problem: from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 6 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 3 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 18 km . then the distance traveled by ferry q is 36 km . ferry q travels at a speed of 9 kph . the time of the journey for ferry q is 36 / 9 = 4 hours , which is 1 hour more than ferry p . the answer is a ."
Answer: a
Python program:
a = 6 * 3
b = 3 * a
c = 6 + 4 
d = b / c
e = d - 3
Problem: 48.95 - 32.006 = ?
Options: a ) 16.089 , b ) 16.35 , c ) 16.89 , d ) 16.944 , e ) none of them
Rationale: "48.950 - 32.006 - - - - - - - - - 16.944 answer is d"
Answer: d
Python program:
a = 48 / 95
b = a * 100
Problem: the effective annual rate of interest corresponding to a nominal rate of 8 % per annum payable half - yearly is ?
Options: a ) 6.06 % , b ) 8.16 % , c ) 6.08 % , d ) 6.09 % , e ) 6.19 %
Rationale: amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 4 / 100 ) 2 ] = rs . 108.16 effective rate = ( 108.16 - 100 ) = 8.16 % answer : b
Answer: b
Python program:
a = 8 / 2
b = 8 / 2
c = a + b 
d = 8 / 2
e = 8 / 2
f = d * e
g = f / 100
h = c + g
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 50 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "legs 10 * 4 = 40 now half on their horses so remaining on the walk so 5 men 5 men has 10 legs so , 10 + 40 = 50 legs walking answer : a"
Answer: a
Python program:
a = 2 / 2
b = 4 + a 
c = 50 / b
Problem: 15.06 * 0.0000001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 1.506 e - 06 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 9 digits should be there . option c"
Answer: c
Python program:
a = 15 / 6
b = a * 100
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 60 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 50 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 60 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 60 * t 3 = 4 hrs t = t 1 + t 2 + t 3 = 17 hrs d = rt ( 240 * 3 ) = r * 17 r = 42.35 answer : c"
Answer: c
Python program:
a = 1 / 80
b = 1 / 24
c = a + b 
d = 1 / 60
e = c + d 
f = 3 / e
Problem: in 1990 the budgets for projects q and v were $ 540000 and $ 780000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30000 and the budget for v was decreased by $ 10000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e .
Answer: e
Python program:
a = 1990 + 4
Problem: a shopkeeper sells 500 metres of cloth for rs . 15000 at a loss of rs . 10 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 40 , b ) s . 12 , c ) s . 96 , d ) s . 50 , e ) s . 13
Rationale: "sp per metre = 15000 / 500 = rs . 30 loss per metre = rs . 10 cp per metre = 30 + 10 = rs . 40 answer : a"
Answer: a
Python program:
a = 15000 / 500
b = a + 10
Problem: in a colony the municipality decided to number the houses and the shops . they want to number the shops with the numbers containing 3 between 1 - 100 . the houses are 10 - 20 floored and at the back of the houses 8 feet is left for fire exit . how many shops can be numbered ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: 3 numbers containing 3 - - - > 3 , 1323 , . . . = 10 numbers - - - - > 30 , 3132 . . . = 10 numbers total = 20 - 1 = 19 answer : a
Answer: a
Python program:
a = 3 * 10
b = a - 10
c = b - 1
Problem: a sporting goods store sold 64 frisbees in one week , some for $ 3 and the rest for $ 4 each . if receipts from frisbee sales for the week totaled $ 196 what is the fewest number of $ 4 frisbees that could have been sold ?
Options: a ) 24 , b ) 12 , c ) 8 , d ) 2 , e ) 4
Rationale: "in this question however , because we are told that exactly 64 frisbees have been sold and revenue was exactly $ 204 , there is only one possible solution for the number of $ 3 and $ 4 frisbees sold . to solve , we have 2 equations and 2 unknowns let x = number of $ 3 frisbees sold let y = number of $ 4 frisbees sold x + y = 64 3 x + 4 y = 196 x = 64 - y 3 ( 64 - y ) + 4 y = 196 192 - 3 y + 4 y = 196 y = 4 answer : e"
Answer: e
Python program:
a = 64 * 3
b = 196 - a
Problem: the average ( arithmetic man ) of 3 integers a , b , and c is exactly half the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 / 2 , c ) 4 , d ) 5 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 1 b / 2 - - > since a = 0 , then ( 0 + b + c ) / 3 = 1 b / 2 - - > c = 3 b / 2 - - > c / b = 3 / 2 . answer : b .
Answer: b
Python program:
a = 1 / 2
b = a * 3
c = b - 1
d = c * 3
Problem: in a room with 10 people , 7 people have exactly 1 friend in the room and 6 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 49 / 45
Rationale: "( 7 / 10 ) ( 8 / 9 ) + ( 6 / 10 ) ( 7 / 9 ) if you choose one of the 7 with one other friend , then you have a 8 / 9 chance of not picking their friend 2 nd . if you choose one of the 6 with 2 friends , you have a 7 / 9 chance of not picking one of their friends second . add them up . 56 / 90 + 42 / 90 98 / 90 = 49 / 45 e . 49 / 45"
Answer: e
Python program:
a = 10 - 1
b = a - 1
c = b - 1
d = 10 - 1
e = c / d
Problem: dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 46 of gas ?
Options: a ) 124 , b ) 256 , c ) 368 , d ) 424 , e ) 512
Rationale: "46 / 4 = 11.5 gallons 11.5 * 32 = 368 miles the answer is c ."
Answer: c
Python program:
a = 46 * 32
b = a / 4
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 6 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 6 / 16 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "# of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 6 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 6 / 5 = 6 - - > total time for both of them would be 10 + 6 = 16 - - > deluxe / total = 6 / 16 . answer : a ."
Answer: a
Python program:
a = 3 + 2 
b = a / 10
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 12 ( t - 3 ) ^ 2 + 120 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 48 , b ) 54 , c ) 60 , d ) 66 , e ) 72
Rationale: "we see that h will be a maximum h = 120 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 12 * ( 5 - 3 ) ^ 2 + 120 = - 12 ( 4 ) + 120 = 72 the answer is e ."
Answer: e
Python program:
a = negate * (
b = 3 + 2 
c = b - 3
d = c ** 2
e = a + d
Problem: if | x - 5 | = 23 what is the sum of all the values of x .
Options: a ) 46 , b ) 10 , c ) 56 , d ) - 46 , e ) 28
Rationale: "there will be two cases x - 5 = 23 and x - 5 = - 23 solve for x = > x = 23 + 5 = > x = 28 or x = - 23 + 5 = > x = - 18 the sum of both values will be 28 + - 18 = 10 answer is b"
Answer: b
Python program:
a = 23 + 5 
b = 23 - 5
c = a - b
Problem: the number of stamps that kaye and alberto had were in the ration of 6 : 4 respectively . after kaye gave alberto 5 of her stamps , the ration of the number of kaye had to the number of alberto had was 8 : 6 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 22 , b ) 25 , c ) 15 , d ) 35 , e ) 30
Rationale: "k 1 = 6 x a 1 = 4 x k 2 = 6 x - 5 a 2 = 4 x + 5 k 2 / a 2 = 8 / 6 ( 6 x - 5 ) / ( 4 x + 5 ) = 8 / 6 6 * ( 6 x - 5 ) = 8 * ( 4 x + 5 ) 36 x - 30 = 32 x + 40 4 x = 70 x = 17.5 k 2 = 6 * 17.5 - 5 = 100 a 2 = 4 * 17.5 + 5 = 75 k 2 - a 2 = 100 - 75 = 25 answer : b"
Answer: b
Python program:
a = 6 + 4 
b = 8 + 6 
c = math.lcm(a, b)
d = 8 + 6 
e = c / d
f = 8 * e
Problem: find √ ? / 11 = 4 ?
Options: a ) 76 , b ) 1936 , c ) 1304 , d ) 1296 , e ) none
Rationale: answer let √ n / 11 = 4 then √ n = 11 x 4 = 44 ∴ n = 44 x 44 = 1936 . correct option : b
Answer: b
Python program:
a = 4 * 11
b = a ** 2
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price w per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Python program:
a = 1 + 1 
b = a * 0
c = 1 + 2 
d = b / c
Problem: two pipes p and q can fill a cistern in 12 and 13 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 4 , d ) 1 / 4 , e ) 3 / 4
Rationale: "3 / 12 + x / 13 = 1 x = 7 3 / 4 answer : e"
Answer: e
Python program:
a = 1 / 12
b = 1 / 13
c = a + b 
d = c * 3
e = 1 - d
f = e * 13
Problem: i flew my tiny seaplane to visit my mother . on the flight up , i flew at 130 mph . on the way home , i flew 88 mph . what was my average speed for the trip ?
Options: a ) 198 mph , b ) 110 mph , c ) 88 mph , d ) 100 mph , e ) 109 mph
Rationale: "( 130 mph + 88 mph ) / 2 = 109 mph correct answer is : e"
Answer: e
Python program:
a = 130 + 88 
b = a / 2
Problem: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 10 % . what was its profit on the items sold in february ?
Options: a ) 27.5 % , b ) 30 % , c ) 35 % , d ) 37.5 % , e ) 40 %
Rationale: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.9 * 150 x = 135 x hence total profit = 35 % option c"
Answer: c
Python program:
a = 100 - 10
b = a / 100
c = 100 + 20 
d = 100 + 25 
e = d / 100
f = c * e
g = b * f
h = g - 100
Problem: if the radius of a circle is decreased 20 % , what happens to the area ?
Options: a ) 10 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 4 / 5 * old radius so new area = ( 4 / 5 ) ^ 2 old area = > 16 / 25 of old area = > 64 % old area answer : c"
Answer: c
Python program:
a = 20 / 100
b = a ** 2
c = b * 100
d = 100 - c
Problem: a man has some hens and cows . if the number of heads be 44 and the number of feet equals 128 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 44 = > h + c = 44 - - - ( equation 1 ) number of feet = 128 = > 2 h + 4 c = 128 = > h + 2 c = 64 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 64 - 44 = > c = 20 substituting the value of c in equation 1 , we get h + 22 = 44 = > h = 44 - 20 = 24 i . e . , number of hens = 24 answer : b"
Answer: b
Python program:
a = 44 * 4
b = a - 128
c = b / 2
Problem: in a 200 meters race a beats b by 35 m or 7 seconds . a ’ s time over the course is :
Options: a ) 40 sec , b ) 47 sec , c ) 33 sec , d ) 35 sec , e ) none of these
Rationale: "solution b runs 35 m in 7 sec . ∴ b covers 200 m in ( 7 / 35 x 200 ) = 40 sec b ’ s time over the course = 40 sec . ∴ a ’ s time over the course = ( 40 - 7 ) sec = 33 sec answer c"
Answer: c
Python program:
a = 7 / 35
b = a * 200
c = b - 7
Problem: a and b can do a piece of work in 8 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 13 1 / 3 , b ) 878 , c ) 30 , d ) 88 , e ) 11
Rationale: "c = 1 / 5 â € “ 1 / 8 = 3 / 40 = > 40 / 3 = 13 1 / 3 days answer : a"
Answer: a
Python program:
a = 5 / 8
b = 5 - a
c = 1/(b)
Problem: - 84 * 29 + 365 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 2071 , e ) none of these
Rationale: "= > - 84 * ( 30 - 1 ) + 365 ; = > - ( 84 * 30 ) + 84 + 365 ; = > - 2520 + 449 = - 2071 . correct option : d"
Answer: d
Python program:
a = negate * (
b = a + 29
Problem: if shares of two persons in profits are rs . 300 and rs . 500 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
Rationale: "total profit = 1000 ratio = 300 / 500 = 3 : 5 answer : b"
Answer: b
Python program:
a = 300 / 500
Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability r that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "r probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Python program:
a = 50 / 2
b = a - 1
c = 50 - 1
d = b / c
e = 50 / 2
f = e / 50
g = d * f
h = g * 2
Problem: a train 270 m long , running with a speed of 108 km / hr will pass a tree in
Options: a ) 12 sec , b ) 9 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 108 x 5 / 18 ) m / sec . = 30 m / sec . time taken = ( 270 x 1 / 30 ) sec = 9 sec answer b"
Answer: b
Python program:
a = 108 * 1000
b = 270 / a
c = b * 3600
Problem: a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 12 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 17
Rationale: "container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 12 ounces in the ratio 1 : 3 or , x + 3 x = 12 gives x ( alcohol ) = 3 and remaining water = 9 mixing both we have alcohol = 4 + 3 and water = 8 + 9 ratio thus alcohol / water = 7 / 17 answer e"
Answer: e
Python program:
a = 1 + 2 
b = 1 / a
c = 12 * b
d = 1 + 3 
e = 1 / d
f = 12 * e
g = c + f 
h = 12 + 12 
i = 1 + 2 
j = 1 / i
k = 12 * j
l = 1 + 3 
m = 1 / l
n = 12 * m
o = k + n 
p = h - o
q = g / p
Problem: a and b invests rs . 3000 and rs . 4500 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 ) 6 : 8 , b ) 9 : 8 , c ) 7 : 9 , d ) 9 : 5 , e ) 1 : 1
Rationale: "( 3 * 6 + 6 * 6 ) : ( 4.5 * 12 ) 54 : 54 = > 1 : 1 answer : e"
Answer: e
Python program:
a = 3000 * 6
b = 3000 * 2
c = b * 6
d = a + c 
e = 6 + 6 
f = 4500 * e
g = d / f
Problem: a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 2 t seconds , then what is the length of the platform ?
Options: a ) 0.5 l , b ) l , c ) 1.5 l , d ) 2 l , e ) 3
Rationale: "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 2 t ( l + p ) / ( l / t ) = 2 t p = l the answer is b ."
Answer: b
Python program:
a = 2 - 1
Problem: on a test average ( arithmetic mean ) test score for 4 students is 85 . what must be 5 th student ' s score that average score for 5 students to be 86 ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: ( 4 * 85 + x ) / 5 = 86 x = ( 5 * 86 ) - ( 4 * 85 ) x = 430 - 340 total score required 430 - 340 = 90 correct answer is c
Answer: c
Python program:
a = 86 * 5
b = 4 * 85
c = a - b
Problem: a 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 300 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 200 / 9 = 500 / 9 x = 300 ans is 300 m answer : b"
Answer: b
Python program:
a = 120 + 80 
b = a * const_0_2778
c = 9 * b
d = c - 200
Problem: sharmila works 10 hours per day on monday , wednesday and friday , and 8 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 460 per week . how much does she earn in dollars per hour ?
Options: a ) 8 , b ) 9 , c ) 9.5 , d ) 10 , e ) 11
Rationale: so , she works 30 hours in 3 days so , she works 16 hours in 2 days so in a week she works 46 hours ( 30 + 16 ) and earns $ 460 so , hourly wage is 460 / 46 = > 10 hence answer will be ( d ) 10
Answer: d
Python program:
a = 10 * 3
b = 8 * 2
c = a + b 
d = 460 / c