euclaise/mathqa_programs huggingface dataset:
Problem: we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 548 . how many green hats did we buy ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 548 . 6 ( 85 - g ) + 7 g = 548 . 510 - 6 g + 7 g = 548 . g = 548 - 510 = 38 . the answer is b ."
Answer: b
Python program:
a = 85 * 6
b = 548 - a
Problem: in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 35 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 13 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 35 m ahead . that means jhon was 35 m away from finishing line when they started together . so he will cover 35 m in 5 seconds . so his speed = 35 / 5 = 7 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 13 seconds . correct answer = a"
Answer: a
Python program:
a = 100 - 35
b = a / 5
Problem: when a train travels at a speed of 110 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 12.5 km , b ) 50 km , c ) 60 km , d ) 8.5 km , e ) 9.5 km
Rationale: "let x be the time reached with the speed 110 km / h 50 km / h - - - - > x + 15 distance is equal so 110 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 110 x = 50 x + 750 so the would be in km and x = 12.5 answer : a"
Answer: a
Python program:
a = 15 / const_60
b = a * 50
c = b / 50
d = const_60 * c
Problem: three runners running around a circular track can complete one revolution in 2 , 4 and 5.5 respectively . when will they meet at starting point ?
Options: a ) 40 h
b ) 44 h
c ) 38 h
d ) 20 h
e ) 22 h
Rationale: time at which they meet at starting point = lcm of 2 , 4 and 5.5 = 44 h answer : b
Answer: b
Python program:
a = 2 * 4
b = a * 5
Problem: 3 bottles contain equal mixtures of spirit and water in the ratio 6 : 1 , 5 : 2 and 3 : 1 respectively . if all the solutions are mixed together , the ratio of spirit to water in the final mixture will be
Options: a ) 64 : 65 , b ) 65 : 64 , c ) 19 : 65 , d ) 65 : 19 , e ) none of these
Rationale: given that all bottles contain equal amount of mixture say v . so in the first vessel - > water : spirit = 1 / 7 : 6 / 7 in the second bottle - > 2 / 7 : 5 / 7 in the third bottle - > l / 4 : 3 / 4 . hence , the final ratio is = ( ( 6 / 7 ) + ( 5 / 7 ) + ( 3 / 4 ) ) / ( ( 1 / 7 ) + ( 2 / 7 ) + ( 1 / 4 ) ) = 65 / 19 answer : d
Answer: d
Python program:
a = 6 + 5 
b = a + 3 
c = 1 + 2 
d = c + 1 
e = b / d
Problem: 12 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 3 , c ) 4 , d ) 7 , e ) 5
Rationale: required number of machines = 12 * 10 / 40 = 3 answer is b
Answer: b
Python program:
a = 12 * 10
b = a / 40
Problem: the age of somu is one - third his father ' s . 10 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 20
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 10 = 3 x - 10 / 5 = x = 20 answer : option e"
Answer: e
Python program:
a = 4 + 1 
b = a * 10
c = b - 10
d = 4 + 1 
e = d - 3
f = c / e
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 8 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 8 x = 45 - - > 27 / 25 * x = 45 - - > x = 45 * 25 / 27 = 125 / 3 = ~ 42 . answer : e ."
Answer: e
Python program:
a = 100 + 8 
b = 100 / a
c = b * 45
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 92.16 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 96
Rationale: "explanation : money collected = ( 92.16 x 100 ) paise = 9216 paise . ∴ number of members = √ ( 9216 ) = 96 . answer : e"
Answer: e
Python program:
a = 92 * 16
b = math.sqrt(a)
Problem: if a person walks at 10 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 20 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 10 5 x - 100 = > x = 20 km . answer : c"
Answer: c
Python program:
a = 10 - 5
b = 20 / a
c = 5 * b
Problem: in a public show 75 % of the seats were filled . if there were 700 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 175 , e ) 150
Rationale: "75 % of 600 = 75 / 100 × 700 = 450 therefore , the number of vacant seats = 700 - 450 = 175 . answer : d"
Answer: d
Python program:
a = 100 - 75
b = 700 * a
c = b / 100
Problem: find the value of m 82519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 825107481 , d ) 725117481 , e ) 477899932
Rationale: "82519 x 9999 = 82519 x ( 10000 - 1 ) = 82519 x 10000 - 82519 x 1 = 825190000 - 82519 = 825107481 c"
Answer: c
Python program:
a = 9999 - 4
b = a * 82519
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ?
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 17 / 27 , d ) 23 / 27 , e ) 65 / 81
Rationale: "p ( missing all 3 ) = ( 2 / 3 ) ^ 4 = 16 / 81 p ( success on at least one attempt ) = 1 - 16 / 81 = 65 / 81 the answer is e ."
Answer: e
Python program:
a = 1 / 3
b = a ** 4
c = 1 - b
Problem: if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 4 , what is the value of k ?
Options: a ) 35 , b ) 40 , c ) 44 , d ) 45 , e ) 56
Rationale: "we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 4 ^ 2 + 3 * 4 - k = 0 k = 32 + 12 = 44 the answer is c"
Answer: c
Python program:
a = 4 ** 2
b = 2 * a
c = 3 * 4
d = b + c
Problem: 4 different airplanes owned by a rock band will be refueling today at the same airport . there are 2 larger planes carrying people and 2 smaller planes carrying equipment . all tanks are empty and will need to be filled completely . the 2 smaller tanks hold 60 liters each and the larger tanks are 50 % bigger . fuel is . 50 cents a liter and there is a charge of $ 100 service for each plane . how much will it cost to fill all 4 planes ?
Options: a ) $ 475 , b ) $ 500 , c ) $ 525 , d ) $ 550 , e ) $ 575
Rationale: lots of calculations . 100 * 4 + 2 * 60 * . 50 + 60 * ( 3 / 2 ) * 2 * . 50 answer = $ 550 the correct option is d
Answer: d
Python program:
a = 100 * 4
b = 2 * 60
c = 60 * 50
d = c / 100
e = d + 60 
f = 2 * e
g = b + f 
h = 1 / 2
i = g * h
j = a + i
Problem: how many litres of pure acid are there in 12 litres of a 40 % solution
Options: a ) 3.6 , b ) 4.8 , c ) 3.5 , d ) 2.3 , e ) 4.4
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 12 * 40 / 100 = 4.8 answer : option b
Answer: b
Python program:
a = 40 / 100
b = a * 12
Problem: a train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 100 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1800 < = > x = 55 speed of the train is 55 kmph . answer : option c"
Answer: c
Python program:
a = 6 * const_0_2778
b = 100 / a
c = b - 5
Problem: line m lies in the xy - plane . the y - intercept of line m is - 4 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 4 ) means line m is parallel to x axis slope m = - 2 ans : a"
Answer: a
Python program:
a = 4 - 8
b = a / 2
c = b + 4 
d = 2 + 6 
e = d / 2
f = c / e
Problem: two pipes a and b can fill a tank in 6 hours and 4 hours respectively . if they are opened on alternate hours and if pipe a is opened first , in how many hours , the tank shall be full ?
Options: a ) 2 hrs , b ) 4 hrs , c ) 5 hrs , d ) 6 hrs , e ) 7 hrs
Rationale: "a ' s work in 1 hour = 1 / 6 b ' s work in 1 hour = 1 / 4 a + b 2 hour ' s work when opened alternately = 1 / 6 + 1 / 4 = 5 / 12 a + b 4 hour ' s work when opened alternately = 10 / 12 = 5 / 6 remaining part = 1 - 5 / 6 = 1 / 6 it is a ' s turn and 1 / 6 part is filled by a in 1 hour . total time taken to fill the tank = 4 + 1 = 5 hrs answer is c"
Answer: c
Python program:
a = 1 / 6
b = 1 / 4
c = a + b 
d = 1 / c
Problem: two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 45 seconds . what is the length of each train ( in meters ) ?
Options: a ) 48.5 , b ) 62.5 , c ) 73.5 , d ) 87.5 , e ) 96.5
Rationale: the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 45 seconds , the relative difference in distance traveled is 45 * 25 / 9 = 125 meters this distance is twice the length of each train . the length of each train is 125 / 2 = 62.5 meters the answer is b .
Answer: b
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 45
e = d / 2
Problem: a certain lab experiments with white and brown mice only . in one experiment , 4 / 9 of the mice are brown . if there are 20 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 26 , c ) 36 , d ) 28 , e ) 24
Rationale: "let total number of mice = m number of brown mice = 4 / 9 m number of white mice = 5 / 9 m = 20 = > m = 36 answer c"
Answer: c
Python program:
a = 4 / 9
b = 20 / a
c = b - 20
Problem: if a + b + c = 21 , what is the total number of non - negative integral solutions ?
Options: a ) 223 , b ) 233 , c ) 240 , d ) 243 , e ) 253
Rationale: think of it is a problem of diving 21 items to three people a , b & c which may or may not receive an item . so simply use combination here as ( n - r + 1 ) c ( r - 1 ) i . e . ( 21 + 3 - 1 ) c ( 3 - 1 ) = > 23 c 2 = = > 253 solutions . answer : e
Answer: e
Python program:
a = 21 + 2 
b = math.factorial(a)
c = math.factorial(21)
d = b / c
e = d / 2
Problem: a driver goes on a trip of 60 kilometers , the first 30 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 42
Rationale: "the time for the first part of the trip was 30 / 48 = 5 / 8 hours . the time for the second part of the trip was 30 / 24 = 5 / 4 hours . the total time fro the trip was 5 / 8 + 5 / 4 = 15 / 8 hours . the average speed for the trip was 60 / ( 15 / 8 ) = 32 kph the answer is b ."
Answer: b
Python program:
a = 30 / 48
b = 60 - 30
c = b / 24
d = a + c 
e = 60 / d
Problem: a train travelled from point a to point b at 160 km / h . on its way back the train travelled at 120 km / h and therefore the trip back lasted one hour longer . what is the distance ( in km ) between a and b ?
Options: a ) 480 . , b ) 500 . , c ) 510 . , d ) 600 . , e ) 800 .
Rationale: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 + 1 thus , s 1 t 1 = s 2 ( t 1 + 1 ) 160 t 1 = 120 ( t 1 + 1 ) t 1 = 3 160 * 3 = 480 answer : a
Answer: a
Python program:
a = 160 - 120
b = 120 / a
c = b + 1 
d = c * 120
Problem: if a is an integer greater than 8 but less than 15 and b is an integer greater than 6 but less than 21 , what is the range of a / b ?
Options: a ) 140 / 217 , b ) 156 / 185 , c ) 217 / 140 , d ) 263 / 149 , e ) 241 / 163
Rationale: the way to approach this problem is 8 < a < 15 and 6 < b < 21 minimum possible value of a is 9 and maximum is 14 minimum possible value of b is 7 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 14 / 7 - 9 / 20 = 217 / 140 hence c
Answer: c
Python program:
a = 15 - 1
b = 6 + 1 
c = a / b
d = 8 + 1 
e = 21 - 1
f = d / e
g = c - f
Problem: the average ( arithmetic mean ) of the integers from 25 to 225 , inclusive , is how much lower than the average of the integers from 50 to 1050 inclusive ?
Options: a ) 450 , b ) 375 , c ) 500 , d ) 425 , e ) 400
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 50 to 1050 , inclusive = ( 50 + 1050 ) / 2 = 550 average of numbers between 25 to 225 , inclusive = ( 25 + 225 ) / 2 = 125 difference = 550 - 125 = 425 answer is d"
Answer: d
Python program:
a = 25 + 225 
b = a / 2
c = 50 + 1050 
d = c / 2
e = b - d
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 5 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 9.6 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 5 machines 5 units of work ( 5 machines ) - - - > 1 hour for 48 units of work 5 * 9.6 - - - > 1 * 9.6 hours e 9.6 hours"
Answer: e
Python program:
a = 6 * 8
b = a / 5
Problem: the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?. a . 27.5 %
Options: a ) 37.2 %
b ) 37.5 %
c ) 30.2 %
d ) 37.7 %
e ) 33.2 %
Rationale: explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b
Answer: b
Python program:
a = 100 + 10 
b = 100 + 25 
c = a * b
d = c / 100
e = d - 100
Problem: the sum of 3 numbers is 98 . if the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8 , then the second number is :
Options: a ) 20 , b ) 30 , c ) 38 , d ) 48 , e ) none of these
Rationale: a : b = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15 and b : c = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24 therefore , a : b : c = 10 : 15 : 24 ∴ a : b : c = 10 : 15 : 24 let the number be 10 x , 15 x and 24 x . then , 10 x + 15 x + 24 x = 98 or 49 x = 98 or x = 2 ⇒ second number = 15 x = 15 × 2 = 30 answer b
Answer: b
Python program:
a = 2 + 3 
b = 8 * 3
c = b / 5
d = a + c 
e = 98 / d
f = e * 3
Problem: if 20 men can build a water fountain 56 metres long in 42 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 3 m , b ) 4 m , c ) 7 m , d ) 9 m , e ) 10 m
Rationale: "explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 42 : 3 : : 56 : x therefore ( 20 x 42 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 840 = 7 hence , the required length is 7 m . answer : c"
Answer: c
Python program:
a = 20 * 42
b = 56 / a
c = 35 * 3
d = b * c
Problem: find large number from below question the difference of two numbers is 1500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1234 , b ) 1345 , c ) 1456 , d ) 1797 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1500 ) . x + 1500 = 6 x + 15 5 x = 1485 x = 297 large number = 297 + 1500 = 1797 d"
Answer: d
Python program:
a = 1500 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: from below option 27 is divisible by which one ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 9 , d ) d ) 10 , e ) e ) 911
Rationale: "27 / 9 = 3 c"
Answer: c
Python program:
a = math.sqrt(27)
Problem: the amounts of time that three secretaries worked on a special project are in the ratio of 2 to 3 to 5 . if they worked a combined total of 80 hours , how many hours did the secretary who worked the longest spend on the project ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 16 , e ) 40
Rationale: "10 x = 80 = > x = 8 therefore the secretary who worked the longest spent 8 x 5 = 40 hours on the project option ( e )"
Answer: e
Python program:
a = 2 + 3 
b = a + 5 
c = 80 / b
d = c * 5
Problem: the ratio of number of boys and girls in a class is 3 : 2 . in the 1 st semester exam 20 % of boys and 25 % of girls get more than or equal to 90 % marks . what percentage of students get less than 90 % marks ?
Options: a ) 56 , b ) 70 , c ) 78 , d ) 80 , e ) 85
Rationale: let boys = 3 x and girls = 2 x . number of those who get less than 90 % mark = ( 80 % of 3 x ) + ( 75 % of 2 x ) = ( 80 / 100 ) * 3 x + ( 75 / 100 * 2 x ) = 39 x / 10 required percentage = ( 39 x / 10 * 1 / 5 x * 100 ) % = 78 % . answer : c
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = b * 3
d = 25 / 100
e = 1 - d
f = e * 2
g = c + f 
h = 3 + 2 
i = g / h
j = i * 100
Problem: if x = 4 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.015 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.015 answer : b"
Answer: b
Python program:
a = 2 / 2
b = a / 1000
Problem: an urn contains 5 red , 6 blue and 8 green balls . 4 balls are randomly selected from the urn , find the probability that the drawn ball are 1 blue and 2 red and 1 green balls ?
Options: a ) 20 / 323 , b ) 40 / 323 , c ) 60 / 273 , d ) 50 / 373 , e ) 40 / 373
Rationale: "sample space = no . of ways 4 balls were drawn from urn = 19 c 4 = 3876 no . ways 1 blue and 2 red and 1 green balls were drawn from bag = 6 c 1 * 5 c 2 * 8 c 1 = 480 probability = 480 / 3876 = 40 / 323 ans - b"
Answer: b
Python program:
a = math.comb(6, 1)
b = math.comb(5, 2)
c = a * b
d = 5 + 6 
e = d + 8 
f = math.comb(e, 4)
g = c / f
Problem: a car takes 6 hours to cover a distance of 504 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: time = 6 distence = 504 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 504 / 9 = 56 kmph d
Answer: d
Python program:
a = 6 * 3
b = a / 2
c = 504 / b
Problem: one - seventh of the light switches produced by a certain factory are defective . 4 - fifths of the defective switches are rejected and 1 / 15 of the non defective switches are rejected by mistake . if all the switches not rejected are sold , what percent of the switches sold by the factory are defective ?
Options: a ) 2.3 % , b ) 3.4 % , c ) 4.5 % , d ) 5.6 % , e ) 6.7 %
Rationale: 1 / 7 of the switches are defective . the defective switches that are not rejected are 1 / 5 * 1 / 7 = 1 / 35 = 3 / 105 of all switches . the non defective switches that are sold are 6 / 7 * 14 / 15 = 84 / 105 of all switches . the percent of switches sold that are defective is 3 / 87 which is about 3.4 % . the answer is b .
Answer: b
Python program:
a = 3 + 4 
b = 1 / a
c = 2 + 3 
d = 1/(c)
e = b * d
f = 15 - 1
g = f / 15
h = 3 + 3 
i = 3 + 4 
j = h / i
k = g * j
l = 3 + 4 
m = 1 / l
n = 2 + 3 
o = 1/(n)
p = m * o
q = k + p 
r = e / q
s = r * 100
Problem: the average of 10 numbers is calculated as 23 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 23 + 36 – 26 = 240 = > 240 / 10 = 24 e )"
Answer: e
Python program:
a = 36 - 26
b = a / 10
c = 23 + b
Problem: a survey was sent to 80 customers , 7 of whom responded . then the survey was redesigned and sent to another 63 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "case 1 : ( 7 / 80 ) = x / 100 x = 9 % case 2 : ( 9 / 63 ) = y / 100 y = 14 % so percent increase is = ( y - x ) = ( 14 - 9 ) % = 5 % answer is b"
Answer: b
Python program:
a = 9 / 63
b = 7 / 80
c = a - b
d = c * 100
e = math.floor(d)
Problem: average age of students of an adult school is 42 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 200 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 42 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 80 so , required no . of students after joining the new students = x + 120 = 200 . answer : d"
Answer: d
Python program:
a = 32 + 4 
b = a * 120
c = 120 * 32
d = b - c
e = 32 + 4 
f = 42 - e
g = d / f
h = g * 4
Problem: you have been given a physical balance and 7 weights of 45 , 50 , 53 , 46 , 52 , 46 and 80 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 188 kgs .
Options: a ) 183 , b ) 185 , c ) 182 , d ) 184 , e ) 181
Rationale: "80 + 52 + 53 = 185 answer : b"
Answer: b
Python program:
a = 50 + 53 
b = a + 46 
c = b + 46
Problem: a person has to make 146 pieces of long bar . he take $ seconds to cut piece . what is total time taken by him to make 146 pieces ?
Options: a ) 580 seconds , b ) 680 seconds , c ) 500 seconds , d ) 540 seconds , e ) 560 seconds
Rationale: if it is 4 seconds , as u have mistaken with shift key , then . . . . we ' ll have to make 145 cuts for 146 pieces . so 145 * 5 = 580 seconds answer : a
Answer: a
Python program:
a = 146 - 1
b = 4 * a
Problem: a tank can supply water to a village for 60 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 45 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 15 , b ) 18 , c ) 20 , d ) 24 , e ) 36
Rationale: losing 10 liters per day results in a loss of 450 liters in 45 days . so , those 450 liters were for 15 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 60 = 1800 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 1800 / 50 = 36 days . the answer is e .
Answer: e
Python program:
a = 10 * 45
b = 60 - 45
c = a / b
d = c * 60
e = 10 * 45
f = 60 - 45
g = e / f
h = 20 + g 
i = d / h
Problem: how many plants will be there in a circular bed whose outer edge measure 32 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 20 , e ) none of these
Rationale: "circumference of circular bed = 32 cm area of circular bed = ( 32 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 32 ) 2 â  „ 4 ï € ã · 4 = 20.36 = 20 ( approx ) answer d"
Answer: d
Python program:
a = 2 * math.pi
b = 32 / a
c = circle_area / (
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 80 kg , d ) 85 kg , e ) 25 kg
Rationale: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 60 + 20 ) kg = 80 kg . answer : c"
Answer: c
Python program:
a = 2 * 5
b = a + 60