euclaise/mathqa_programs huggingface dataset:
Problem: a and b together can complete work in 4 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 4 now a does half of the work in 3 days so a can complete the whole work in 6 days a ’ s one day work = 1 / 6 b ’ s one day work = 1 / 4 - 1 / 6 = 1 / 12 b alone can complete the work in 12 days so half of the work in 6 days answer : option d"
Answer: d
Python program:
a = 3 / 4
b = 4 * a
Problem: sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 1 % more . she would get how much ?
Options: a ) 9440 , b ) 96288 , c ) 26667 , d ) 1662 , e ) 2882
Rationale: "( 8000 * 3 * 1 ) / 100 = 240 9200 - - - - - - - - 9440 answer : a"
Answer: a
Python program:
a = 1 / 100
b = 9200 - 8000
c = b / 3
d = c / 8000
e = a + d 
f = e * 8000
g = f * 3
h = g + 8000
Problem: john is 3 times as old as sam . if john will be twice as old as sam in 9 years , how old was sam two years ago ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 7
Rationale: j = 3 s after 9 years j + 9 = 2 ( s + 9 ) j = 2 s + 9 2 s + 9 = 3 s s = 9 two years ago s = 9 - 2 = 7 e is the answer
Answer: e
Python program:
a = 2 * 9
b = a - 9
c = b - 2
Problem: a bowl of fruit contains 14 apples and 23 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 6 , c ) 14 , d ) 17 , e ) 20
Rationale: number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 23 - x ) = 37 - x 14 / ( 37 - x ) = 7 / 10 = > 20 = 37 - x = > x = 17 answer d
Answer: d
Python program:
a = 14 + 23 
b = 70 / 100
c = a * b
d = c - 14
e = 70 / 100
f = d / e
Problem: √ ( 49 ) 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 49 ) 2 = ? or , ? = 49 answer c"
Answer: c
Python program:
a = 49 ** 2
b = math.sqrt(a)
Problem: one woman and one man can build a wall together in three hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them five hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 2 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 3 - - > ( 1 ) , w + 2 g = 1 / 3 - - > ( 2 ) and m + g = 1 / 5 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 15 , m = 2 / 15 and w = 1 / 5 . so , n = 1 / ( 2 / 5 ) = 5 / 2 option , a"
Answer: a
Python program:
a = 4 + 1 
b = a + 4 
c = 1/(b)
d = 4 + 1 
e = 1/(d)
f = e * 2
g = c + f 
h = g / 2
i = 4 + 1 
j = 1/(i)
k = h - j
l = 3 / 2
m = k / l
n = 4 + 1 
o = 1/(n)
p = m + o 
q = 1/(p)
Problem: two trains each 170 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 55 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 15 sec , b ) 11.6 sec , c ) 31.6 sec , d ) 12.6 sec , e ) 23 sec
Rationale: explanation : d = 170 m + 170 m = 340 m rs = 55 + 50 = 105 * 5 / 18 = 146 / 5 t = 340 * 5 / 146 = 11.6 sec answer : option b
Answer: b
Python program:
a = 170 + 170 
b = a / 1000
c = 55 + 50 
d = b / c
e = 3600 * d
Problem: 8 cups of water are to be poured into a 4 - cup bottle and a 8 - cup bottle . if each bottle is to be filled to the same fraction of its capacity , how many cups of water should be poured into the 8 - cup bottle ?
Options: a ) 2 / 3 , b ) 7 / 3 , c ) 5 / 2 , d ) 8 / 3 , e ) 16 / 3
Rationale: let x be the # of cups going into the 8 cup bottle . so . . . . x / 8 = ( ( 8 - x ) / 4 ) 64 - 8 x = 4 x 64 = 12 x x = 16 / 3 . answer : e
Answer: e
Python program:
a = 8 * 2
b = 4 + 2 
c = a / b
d = c * 2
Problem: a candidate got 30 % of the votes polled and he lost to his rival by 4000 votes . how many votes were cast ?
Options: a ) 7500 , b ) 2028 , c ) 2775 , d ) 10000 , e ) 6851
Rationale: "30 % - - - - - - - - - - - l 70 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 40 % - - - - - - - - - - 4000 100 % - - - - - - - - - ? = > 10000 answer : d"
Answer: d
Python program:
a = 30 / 100
b = 1 - a
c = 30 / 100
d = b - c
e = 4000 / d
Problem: the average age of a group of n people is 14 years old . one more person aged 32 joins the group and the new average is 15 years old . what is the value of n ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "14 n + 32 = 15 ( n + 1 ) n = 17 the answer is e ."
Answer: e
Python program:
a = 32 - 15
b = 15 - 14
c = a / b
Problem: the average of 7 numbers is 26 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 130
Rationale: "explanation : average of new numbers = 26 * 5 = 130 answer : option e"
Answer: e
Python program:
a = 26 * 5
Problem: if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 345 , the cost of the article is
Options: a ) 289 , b ) 231 , c ) 100 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 345 = 5 x / 20 = 5 = > x = 100 answer : c"
Answer: c
Python program:
a = 350 - 345
b = 5 / 100
c = a / b
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 4 . if the sum of their ages is 88 , what is the difference between the ages of patrick and monica ?
Options: a ) 22 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x : 5 x ages of mi and mo = 3 x : 4 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 20 x sum = 44 x = 88 x = 2 difference if ages of pa and mo = 20 x - 9 x = 11 x = 11 * 2 = 22 answer a"
Answer: a
Python program:
a = 4 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 4 * 5
f = d + e 
g = 88 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 4 * 5
n = l + m 
o = 88 / n
p = i * o
q = h - p
Problem: 14 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 189 , e ) 45
Rationale: "there are 14 business exec and in each handshake 2 business execs are involved . hence 14 c 2 = 91 also , each of 14 exec will shake hand with every 7 other chairmen for total of 98 handshake . total = 91 + 98 = 189 ans : d"
Answer: d
Python program:
a = 14 - 1
b = 14 * a
c = b / 2
d = 14 * 7
e = c + d
Problem: 5 n - 3 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9
Rationale: 5 n - 3 > 12 5 n > 15 n > 3 7 n - 5 < 44 7 n < 49 n < 7 so n must be between 3 and 7 3 < n < 7 correct answer d
Answer: d
Python program:
a = 5 + 44 
b = a / 7
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 12 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 12 . then 4 n < 12 and n < 3 . the largest possible integer is n = 2 . the answer is b ."
Answer: b
Python program:
a = 5 - 1
b = 12 / a
c = math.floor(b)
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 11 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 6.24 , b ) 7.4 , c ) 7.92 , d ) 6.28 , e ) 7.24
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 11 ) = 7 / 44 the cistern will be filled in 44 / 7 hrs i . e . , 6.28 hrs . answer : d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 11
c = a - b
d = 1 / c
Problem: what is 3 / 7 of 7 / 8 of 1 / 3 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 9 / 16 , d ) 1 / 8 , e ) 16 / 9
Rationale: 3 / 7 * 7 / 8 * 1 / 3 = 1 / 8 answer : d
Answer: d
Python program:
a = 3 / 7
b = 7 / 8
c = 1 / 3
d = b * c
e = a * d
Problem: the least number which should be added to 2400 so that the sum is exactly divisible by 5 , 6,4 and 3 is :
Options: a ) 3 , b ) 13 , c ) 20 , d ) 33 , e ) 43
Rationale: solution l . c . m . of 5 , 6,4 and 3 = 60 . on dividing 2400 by 60 , the remainder is 40 . ∴ number to be added = ( 60 - 40 ) = 20 . answer c
Answer: c
Python program:
a = 2 * 2
b = a * 5
c = b * 3
d = 2 * 2
e = d * 5
f = e * 3
g = 2400 / f
h = c - g
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 82 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 8400 , b ) 8200 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 82 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 82 = > total appeared candidates in state b = 82 x 100 = 8200 = > total appeared candidates in state a = total appeared candidates in state b = 8200"
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 82 / b
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 28 sec , b ) 16 sec , c ) 34 sec , d ) 18 sec , e ) 17 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 100 = 340 m . time taken = 340 / 10 = 34 sec . answer : c"
Answer: c
Python program:
a = 240 + 100 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 8720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2991
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 8720 32.5 k = 32.5 k / 100 k * 8720 = 2834 the number of valid votes polled in favour of b is 2834 . answer : c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = b * 8720
d = 15 * 8720
e = d / 100
f = c - e
g = f / 2
Problem: a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1200 , b ) $ 1005.8 , c ) $ 555.6 , d ) $ 1009.2 , e ) $ 1490.7
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2500 = $ 555.6"
Answer: c
Python program:
a = 1/(8)
b = 1/(12)
c = 1/(6)
d = 1/(8)
e = c + d 
f = b + e 
g = a / f
h = 2500 * g
Problem: 23 , 29 , 31 , 37 , 41 , 43 , ( . . . )
Options: a ) 53 , b ) 48 , c ) 59 , d ) 47 , e ) 50
Rationale: "all are prime numbers in their order , starting from 23 hence , next number is 47 answer is d"
Answer: d
Python program:
a = negate - (
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 81 . how much was lent at 5 % ?
Options: a ) 299 , b ) 666 , c ) 778 , d ) 900 , e ) 977
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 81 5 x / 100 + 90 – 6 x / 100 = 81 x / 100 = 9 = > x = 900 answer : d"
Answer: d
Python program:
a = 5 + 6 
b = a * 100
Problem: what will be the difference between simple and compound interest at 16 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 164.19 , b ) 164.12 , c ) 170.6 , d ) 167.1 , e ) 165.11
Rationale: "s . i . = ( 1000 * 16 * 4 ) / 100 = rs . 640 c . i . = [ 1000 * ( 1 + 16 / 100 ) 4 - 1000 ] = rs . 810.6 difference = ( 810.6 - 640 ) = rs . 170.6 answer : c"
Answer: c
Python program:
a = 16 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 16 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: in what time will a train 350 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.95 sec , c ) 1.3 sec , d ) 8.75 sec , e ) 1.85 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 100 / 40 = 8.75 sec . answer : d"
Answer: d
Python program:
a = 144 * const_0_2778
b = 350 / a
Problem: an aeroplane covers a certain distance of 530 kmph in 5 hours . to cover the same distance in 3 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 640 , d ) 722 , e ) 250
Rationale: "speed of aeroplane = 530 kmph distance travelled in 5 hours = 530 * 5 = 2650 km speed of aeroplane to acver 2650 km in 11 / 3 = 2650 * 3 / 11 = 722 km answer d"
Answer: d
Python program:
a = 530 * 5
b = 3 * 3
c = b + 2 
d = c / 3
e = a / d
Problem: there are 4 red books and 4 blue books on a shelf . if 2 books are selected at random from the shelf , what is the probability that both books selected are red books ?
Options: a ) 2 / 7 , b ) 3 / 7 , c ) 3 / 14 , d ) 5 / 28 , e ) 9 / 28
Rationale: the number of ways of choosing 2 books from the shelf is 8 c 2 = 28 . the number of ways of choosing 2 red books is 4 c 2 = 6 . p ( 2 red books ) = 6 / 28 = 3 / 14 . the answer is c .
Answer: c
Python program:
a = 4 + 4 
b = 4 / a
c = 4 - 1
d = 4 + 4 
e = d - 1
f = c / e
g = b * f
Problem: on a ranch , a rancher can place a loop of rope , called a lasso , once in every 2 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 ) 3 / 4 , b ) 5 / 8 , c ) 7 / 8 , d ) 11 / 16 , e ) 15 / 16
Rationale: p ( missing all 4 ) = ( 1 / 2 ) ^ 4 = 1 / 16 p ( success on at least one attempt ) = 1 - 1 / 16 = 15 / 16 the answer is e .
Answer: e
Python program:
a = 1 / 2
b = a ** 4
c = 1 - b
Problem: a no . when divided by 222 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 10 , e ) 15
Rationale: "222 + 43 = 265 / 17 = 10 ( remainder ) d"
Answer: d
Python program:
a = 222 + 43 
b = a / 17
Problem: the ratio of the arithmetic mean of two numbers to one of the numbers is 4 : 7 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 8 , b ) 1 : 7 , c ) 1 : 6 , d ) 1 : 5 , e ) 1 : 4
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 4 : 7 , thus the smaller number must have a ratio of 1 . the ratio of the smaller number to the larger number is 1 : 7 . the answer is b ."
Answer: b
Python program:
a = 4 / 7
b = 1 / 2
c = a - b
d = c * 2
Problem: when magnified 1,000 times by an electron microscope , the image of a certain circular piece of tissue has a diameter of 5 centimeter . the actual diameter of the tissue , in centimeters , is
Options: a ) 0.005 , b ) 0.002 , c ) 0.001 , d ) 0.0005 , e ) 0.0002
Rationale: "it is very easy if x is the diameter , then the magnified length is 1000 x . ince 1000 x = 5 then x = 5 / 1000 = 0.005 . the answer is a"
Answer: a
Python program:
a = 5 / 1
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 265 m long ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 77 , e ) 21
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 265 = 625 m required time = 625 * 2 / 25 = 50 sec answer : a"
Answer: a
Python program:
a = 45 - 265
b = a * const_0_2778
c = 360 / b
Problem: if the sales tax be reduced from 4 ( 1 / 2 ) % to 3 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 10500 ?
Options: a ) rs . 105 , b ) rs . 150 , c ) rs . 146 , d ) rs . 135 , e ) none of these
Rationale: "explanation : required difference = ( 4 ( 1 / 2 ) of rs . 10500 ) - ( 3 ( 1 / 2 ) of rs . 10500 ) = ( 9 / 2 – 7 / 2 ) % of rs . 10500 = ( 1 ) x ( 1 / 100 ) x 10500 = rs . 105 answer a"
Answer: a
Python program:
a = 3 / 4
b = 4 + a 
c = b / 100
d = c + 1 
e = 1 / 2
f = e + 1 
g = f / 100
h = g + 1 
i = 10500 / h
j = d * i
k = j - 10500
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 151 ?
Options: a ) 2050 , b ) 2350 , c ) 2650 , d ) 2950 , e ) 3250
Rationale: "100 + 102 + . . . + 150 = 100 * 26 + ( 2 + 4 + . . . + 50 ) = 100 * 26 + 2 * ( 1 + 2 + . . . + 25 ) = 100 * 26 + 2 ( 25 ) ( 26 ) / 2 = 100 * 26 + 25 * 26 = 125 ( 26 ) = 3250 the answer is e ."
Answer: e
Python program:
a = 151 - 1
b = 99 + 1 
c = a - b
d = c / 2
e = d + 1
Problem: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 3 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 140
Rationale: "rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 3 of all one - bedroom : 1 / 3 * { all one bedroom } = 40 - - > { all one - bedroom } = 120 { all two - bedroom } = 490 - 120 = 370 . two - bedroom not rented = 370 - 240 = 130 answer : d ."
Answer: d
Python program:
a = 490 / 7
b = 4 * a
c = 490 / 7
d = 4 * c
e = 3 + 1 
f = d / e
g = 3 * f
h = b - g
i = 1 / 3
j = h / i
k = 490 - j
l = 490 / 7
m = 4 * l
n = 3 + 1 
o = m / n
p = 3 * o
q = k - p
Problem: if six machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 72 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 6 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 4 = 10 / 3 * x x = 6 / 5 hour so 72 minutes answer : c"
Answer: c
Python program:
a = 3 / 5
b = 3 / 4
c = b / 5
d = c / 30
e = d * 2
f = a / e
Problem: a fill pipe can fill 1 / 2 of cistern in 30 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 15 min , b ) 20 min , c ) 25 min , d ) 30 min , e ) 35 min
Rationale: "required time = 30 * 2 * 1 / 2 = 30 minutes answer is d"
Answer: d
Python program:
a = 30 / 1
Problem: the value of ( 4.7 × 13.26 + 4.7 × 9.43 + 4.7 × 77.31 ) is
Options: a ) 0.47 , b ) 47 , c ) 470 , d ) 4700 , e ) none
Rationale: "solution given expression = 4.7 × ( 13.26 + 9.43 + 77.31 ) = 4.7 × 100 = 470 . answer c"
Answer: c
Python program:
a = 13 + 26 
b = a + 77 
c = 4 * 7
Problem: a is 30 % more efficient than b . how much time will they working together take to complete a job which a alone could have done in 23 days ?
Options: a ) 11 , b ) 13 , c ) 20 3 / 17 , d ) 14 , e ) none of these
Rationale: explanation : ratio of times taken by a and b = 100 : 130 = 10 : 13 suppose b takes x days to work the 10 : 13 : : 23 : x = > x = 23 x 13 / 10 = 299 / 10 a ’ s one day work = 1 / 23 and b ’ s is 10 / 299 then a + b ‘ s work = 1 / 23 + 10 / 299 = 23 / 299 = 1 / 13 = > 13 days answer : option b
Answer: b
Python program:
a = 1 / 23
b = 30 / 100
c = b + 1 
d = c * 23
e = 1 / d
f = a + e 
g = 1/(f)
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 . 2445 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 815 , d ) s . 900 , e ) s . 920
Rationale: "2445 * 1 / 3 = 815 option c"
Answer: c
Python program:
a = 1 / 3
b = 2445 * a
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 18 km , d ) 60 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 15 5 x - 300 = > x = 60 km . answer : d"
Answer: d
Python program:
a = 15 - 10
b = 20 / a
c = 10 * b
Problem: gwen drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 30 miles / hr for the remaining 40 miles of the trip if she made no stops during the trip what was gwen ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 80 miles total time = 40 / 15 + 40 / 30 = 4 avg . speed = 20 . answer - b
Answer: b
Python program:
a = 40 + 40 
b = 40 / 15
c = 40 / 30
d = b + c 
e = a / d
Problem: a boat m leaves shore a and at the same time boat b leaves shore b . they move across the river . they met at 500 yards away from a and after that they met 300 yards away from shore b without halting at shores . find the distance between the shore a & b .
Options: a ) 1100 yards , b ) 1200 yards , c ) 1300 yards , d ) 1400 yards , e ) 1000 yards
Rationale: "if x is the distance , a is speed of a and b is speed of b , then ; 500 / a = ( x - 500 ) / b and ( x + 300 ) / a = ( 2 x - 300 ) / b , solving it , we get x = 1200 yards answer : b"
Answer: b
Python program:
a = 300 * 4
Problem: 78 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "78 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 78 = 80 , 48 = 50 , 25,075 = 25,000 are derived , which makes ( 78 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is b ."
Answer: b
Python program:
a = 78 * 48
b = const_0_25 * 1000
c = b * 100
d = 3 + 4 
e = d * 10
f = c + e 
g = f + 3 
h = a * g
Problem: the average salary / head of all the workers in a workshop is rs . 1000 , if the average salary / head of 10 technician is rs . 1200 and the average salary / head of the rest is rs . 820 , the total no . of workers in the work - shop is ?
Options: a ) 120 / 9 , b ) 140 / 9 , c ) 150 / 9 , d ) 190 / 9 , e ) 170 / 9
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 10 technician + sum of salary for other y - 10 workers . 10 x 1200 + 820 ( y - 10 ) = 1000 y ⇒ 12000 + 820 y - 8200 = 1000 y ⇒ 180 y = 3800 ∴ y = 190 / 9 so total number of workers = 190 / 9 d
Answer: d
Python program:
a = 10 * 1200
b = 820 * 10
c = a - b
d = 1000 - 820
e = c / d