euclaise/mathqa_programs huggingface dataset:
Problem: the average of 100 , 200300 and x is 250 and the average of 300 , 150100 , x and y is 200 . what is the value of y ?
Options: a ) 100 , b ) 150 , c ) 50 , d ) 200 , e ) 250
Rationale: we have : ( 100 + 200 + 300 + x ) / 4 = 250 600 + x = 1000 x = 400 ( 300 + 150 + 100 + x + y ) / 5 = 200 550 + 400 + y = 1000 y = 50 answer is c
Answer: c
Python program:
a = 3 + 2 
b = 200 * a
c = 250 - 100
d = 300 + c 
e = d + 100 
f = 250 * 4
g = f - 100
h = 2 * 100
i = g - h
j = 3 * 100
k = i - j
l = e + k 
m = b - l
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 500 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1250 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 500 = 1250 answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1 / 3
d = 1 - c
e = d / 5
f = b - e
g = 1 / 3
h = 1 - g
i = 1 / 3
j = 1 - i
k = j / 5
l = h - k
m = l / 4
n = f - m
o = 500 / n
Problem: a passenger train takes two hours less for a journey of 300 km if its speed is increased by 5 kmph from its normal speed . the normal speed is
Options: a ) 35 kmph , b ) 50 kmph , c ) 25 kmph , d ) 30 kmph , e ) 38 kmph
Rationale: let normal speed = x increased speed = x + 5 initial = > x = 300 / t 1 = > t 1 = 300 / x after = > ( x + 5 ) = 300 / ( t 1 - 2 ) = > ( x + 5 ) = 300 / [ ( 300 / x ) - 2 ] = > x = 25 kmph answer : c
Answer: c
Python program:
a = 5 * 5
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 54 seconds . what is the length of each train ( in meters ) ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 54 seconds , the relative difference in distance traveled is 54 * 25 / 9 = 150 meters this distance is twice the length of each train . the length of each train is 150 / 2 = 75 meters the answer is d ."
Answer: d
Python program:
a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 54
e = d / 2
Problem: the jogging track in a sports complex is 660 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 ) 4.8 min , e ) 5.988 min
Rationale: "clearly , the two will meet when they are 660 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 660 m apart , they take ( 100 / 825 * 660 / 1000 ) hrs = ( 660 / 8250 * 60 ) min = 4.8 min . answer : d"
Answer: d
Python program:
a = 660 / 1000
b = 4 + 5 
c = a / b
d = c * const_60
Problem: in a room with 9 people , 6 people have exactly 1 friend in the room and 5 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 ) 1
Rationale: "( 6 / 9 ) ( 7 / 8 ) + ( 5 / 9 ) ( 6 / 8 ) if you choose one of the 6 with one other friend , then you have a 7 / 8 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 8 chance of not picking one of their friends second . add them up . 42 / 72 + 30 / 72 72 / 72 = 1 e . 1"
Answer: e
Python program:
a = 9 - 1
b = a - 1
c = b - 1
d = 9 - 1
e = c / d
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 20 , 60 , and what number ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 80 = 25 a"
Answer: a
Python program:
a = 20 + 40 
b = a + 60 
c = 5 * 3
d = c + 20 
e = d + 60 
f = b - e
Problem: a and b started a business investing rs . 92,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 23 : 5 , d ) 18 : 4 , e ) 17 : 4
Rationale: a : b = 92000 : 20000 = 92 : 20 = 46 : 10 = 23 : 5 answer : c
Answer: c
Python program:
a = 3 * 3
b = 3 * 3
c = b + 1 
d = a * c
e = d + 2 
f = 3 * 3
g = f + 1 
h = 2 * g
i = e / h
Problem: the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 15 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 13 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 85 y thus 75 x = 85 y or x = 1.13 y ans r = 113 y so increase = 13 % answer : d"
Answer: d
Python program:
a = 100 - 25
b = 100 - 15
c = a / b
d = c * 100
e = 100 - d
f = 100 - 25
g = 100 - 15
h = f / g
i = h * 100
j = e / i
k = j * 100
Problem: if a large pizza has a radius that is 20 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 20 % , b ) 36 % , c ) 44 % , d ) 50 % , e ) 64 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.2 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.2 * r ) ^ 2 = 1.44 * pi * r ^ 2 , an increase of 44 % . the answer is c ."
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: how many cubes of 5 cm edge can be cut out of a cube of 15 cm edge
Options: a ) 36 , b ) 232 , c ) 27 , d ) 48 , e ) none of these
Rationale: "explanation : number of cubes = ( 15 x 15 x 15 ) / ( 5 x 5 x 5 ) = 27 answer : c"
Answer: c
Python program:
a = volume_cube / (
Problem: 160 is what percent of 50 ?
Options: a ) 5 % , b ) 20 % , c ) 320 % , d ) 200 % , e ) 500 %
Rationale: "50 * x = 160 - - > x = 3.2 - - > 3.2 expressed as percent is 320 % . answer : c ."
Answer: c
Python program:
a = 160 / 50
b = a * 100
Problem: a precious stone weighing 35 grams worth rs . 12,250 is accidentally dropped and gets broken into two pieces having weights in the ratio of 2 : 5 . if the price varies as the square of the weight then find the loss incurred .
Options: a ) rs . 5750 , b ) rs . 6000 , c ) rs . 5500 , d ) rs . 5000 , e ) rs . 7000
Rationale: the price varies as the square of the weight , p = k x w 2 12250 = k x 352 k = 10 thus , p = 10 w 2 when the two pieces are in the ratio 2 : 5 ( weight wise ) then we know that their weights must be 10 g and 25 g respectively . their values should be : 10 g piece : 10 x 102 = rs . 1000 ; 25 g piece : 10 x 252 = rs . 6250 . total value of stone now , = 1000 + 6250 = rs . 7250 loss incurred = 12250 - 7250 = rs . 5000 answer : d
Answer: d
Python program:
a = 100 * 100
b = 100 * 100
c = b / 2
d = c / 2
e = a + d 
f = e - 100
g = f - 100
h = 100 / 2
i = g - h
j = 100 * 100
k = 100 * 100
l = k / 2
m = l / 2
n = j + m 
o = n - 100
p = o - 100
q = 100 / 2
r = p - q
s = 35 ** 2
t = r / s
u = 5 * 2
v = u ** 2
w = t * v
x = 100 * 100
y = 100 * 100
z = y / 2
A = z / 2
B = x + A 
C = B - 100
D = C - 100
E = 100 / 2
F = D - E
G = 35 ** 2
H = F / G
I = 5 * 5
J = I ** 2
K = H * J
L = w + K 
M = i - L
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 1 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) = 0.25 answer : d"
Answer: d
Python program:
a = 1 / 4
b = a ** 1
Problem: find the least number must be subtracted from 5474827 so that remaining no . is divisible by 12 ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 7 , e ) 2
Rationale: "on dividing 5474827 by 12 we get the remainder 7 , so 7 should be subtracted d"
Answer: d
Python program:
a = 5474827 / 12
b = math.floor(a)
c = b * 12
d = 5474827 - c
Problem: how many even integers from 1 to 200 ( both inclusive ) have even number of factors ?
Options: a ) 13 , b ) 14 , c ) 5 , d ) 6 , e ) 7
Rationale: "integers having even number of factors will be perfect squares . even numbers will have even perfect squares . thus , the possible values for the perfect squares are : 4 , 16,36 , 64,100 , 144,196 and the corresponding integers are 2 , 4,6 , 8,10 , 12,14 ( more than 6 ) . thus e is the correct answer ."
Answer: e
Python program:
a = math.sqrt(200)
b = a / 2
Problem: working alone , pump a can empty a pool in 6 hours . working alone , pump b can empty the same pool in 9 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 192 , b ) 200 , c ) 208 , d ) 216 , e ) 224
Rationale: "pump a can empty ( 1 / 6 ) of the pool per hour . pump b can empty ( 1 / 9 ) of the pool per hour . together the pumps can empty 1 / 6 + 1 / 9 = 5 / 18 of the pool per hour . 1 pool / ( 5 / 18 ) pool per hour = 18 / 5 hours = 216 minutes . the answer is d ."
Answer: d
Python program:
a = 1 / 6
b = 1 / 9
c = a + b 
d = 1/(c)
e = d * const_60
Problem: a bakery has 6 employees . it pays annual salaries of $ 18,000 to each of 2 employees , $ 20,000 to 1 employee , and $ 21,000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
Options: a ) $ 19,200 , b ) $ 19,500 , c ) $ 19,800 , d ) $ 20,000 , e ) $ 20,400
Rationale: "average = 2 ( 18000 ) + ( 20000 ) + 3 ( 21000 ) / 6 = $ 19,833 the answer is c ."
Answer: c
Python program:
a = 10 + 10 
b = a + 1 
c = b + 1 
d = c * 3
e = 10 + 10 
f = e - 1
g = f * 2
h = d + g 
i = 10 + 10 
j = i + 1 
k = h + j 
l = k / 6
Problem: a box contains 4 black , 3 red and 6 green marbles . 3 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 24 / 286 , b ) 25 / 709 , c ) 25 / 286 , d ) 24 / 268 , e ) 24 / 226
Rationale: "explanation : total marbles in a box = 4 black + 3 red + 6 green marbles = 13 marbles 3 marbles are drawn from 13 marbles at random . therefore , n ( s ) = 13 c 3 = 286 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 4 c 3 + 3 c 3 + 6 c 3 = 4 + 1 + 20 = 25 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 25 / 286 answer : c"
Answer: c
Python program:
a = 3 + 6 
b = 3 + 3 
c = 10 + b 
d = a + c 
e = 10 + 3 
f = e * 6
g = d / f
Problem: annika hikes at a constant rate of 10 minutes per kilometer . she has hiked 2.5 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 45 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 45 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "set up two r x t = d cases . 1 . 1 / 10 km / min x t = 2.5 from which t = 25 mins . we know total journey time now is 45 + 25 = 70 the rate is the same ie 1 / 10 km / min . set up second r x t = d case . 1 / 10 km / min x 70 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 b ."
Answer: b
Python program:
a = 45 / 10
b = a - 2
c = b / 2
d = c + 2
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 18 of money ?
Options: a ) 1800 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 18 ( 100 / 10 ) 2 = > p = 1800 answer : a"
Answer: a
Python program:
a = 10 * 2
b = 18 / a
c = b * 100
d = 10 * 2
e = c * d
Problem: 544 , 509 , 474 , 439 , . . . ?
Options: a ) 404 , b ) 302 , c ) 108 , d ) 115 , e ) 210
Rationale: "each number is 35 less than the previous number . 544 544 - 35 = 509 509 - 35 = 474 474 - 35 = 439 439 - 35 = 404 answer : a"
Answer: a
Python program:
a = negate - (
Problem: if the sum of a number and its square is 182 , what is the number ?
Options: a ) 15 , b ) 26 , c ) 28 , d ) 91 , e ) none of these
Rationale: "let the number be x . then , x + x 2 = 182 ( x + 14 ) ( x - 13 ) = 0 x = 13 answer : e"
Answer: e
Python program:
a = math.sqrt(182)
b = math.floor(a)
Problem: the difference between compound and simple interest on a certain sum of money for 3 years at 6 2 / 3 % p . a is rs . 184 . find the sum ?
Options: a ) 33772 , b ) 26782 , c ) 26788 , d ) 13500 , e ) 27761
Rationale: p = ( 184 * 106 ) / [ 6 2 / 3 * 6 2 / 3 * ( 300 * 6 2 / 3 ) ] p = 13500 answer : d
Answer: d
Python program:
a = 184 * 3
b = a * 3
c = b * 3
d = c * 6
e = d / 2
f = e - 1000
Problem: a block of wood has dimensions 10 cm x 10 cm x 80 cm . the block is painted red and then cut evenly at the 40 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5.6 %
b ) 8.4 %
c ) 11.2 %
d ) 14.8 %
e ) 17.5 %
Rationale: the area of each half is 100 + 4 ( 400 ) + 100 = 1800 the area that is not painted is 100 . the fraction that is not painted is 100 / 1800 = 1 / 18 = 5.6 % the answer is a .
Answer: a
Python program:
a = 4 * 100
b = a * 4
c = b + 100 
d = c + 100 
e = 100 / d
f = e * 100
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 3200 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 3200 x = ( 2 ^ 7 * 25 ) / 2 ^ 9 = 25 / 4 the answer is b ."
Answer: b
Python program:
a = const_60 / 2
b = a + const_60 
c = b / 10
d = c - 1
e = 2 ** d
f = 3200 / e
g = f / 2
Problem: a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 45 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 33 % . , e ) 51 % .
Rationale: "30 % of 2 litres = 0.6 litres 45 % of 6 litres = 2.7 litres therefore , total quantity of alcohol is 3.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 33 % d"
Answer: d
Python program:
a = 30 / 100
b = a * 2
c = 45 / 100
d = c * 6
e = b + d 
f = e / 10
g = f * 100
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 60 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 89 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 60 % more than company a ' s assets which is 160 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 80 a + b = 180 kw = 160 kw / ( a + b ) * 100 = 160 / 180 * 100 = 88.88 % or 89 % c"
Answer: c
Python program:
a = 100 + 60 
b = 100 + 60 
c = b / 2
d = 100 + c 
e = a / d
f = e * 100
Problem: a certain rectangular window is ( 2 / 5 ) times as long as it is wide . if its perimeter is 28 feet , what are its dimensions in terms of length by width ?
Options: a ) 12 by 2 , b ) 11 by 3 , c ) 10.5 by 3.5 , d ) 10 by 4 , e ) 9 by 3
Rationale: "2 x + 2 y = 28 x + y = 14 x + ( 2 / 5 ) x = 14 1.4 x = 14 x = 10 answer d"
Answer: d
Python program:
a = 10 + 2
Problem: a person travels equal distances with speeds of 5 km / hr , 6 km / hr and 7 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 5 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 5 + x / 6 + x / 7 = 27 / 53 27 x / 53 = 47 / 60 = > x = 1.54 total distance = 3 * 1.54 = 4.61 km . answer : a"
Answer: a
Python program:
a = 47 / const_60
b = 1 / 5
c = 1 / 6
d = b + c 
e = 1 / 7
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: if the a radio is sold for rs 490 and sold for rs 465.50 . find loss value .
Options: a ) 24.5 , b ) 12.5 , c ) 17.25 , d ) 6.5 , e ) 13.62
Rationale: "cp = rs 490 , sp = 465.50 . loss = rs ( 490 - 465.50 ) = rs 24.50 . ans : a"
Answer: a
Python program:
a = 490 - 465
b = a / 490
c = b * 100
Problem: set s consists of integers { 4 , 7 , 10 , 14 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 50 % . what is the value of integer n ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the average of the numbers in set s is 10 . if we increase the mean by 50 % , the new mean is 15 . thus , on average , 5 numbers increase by 5 . therefore n = 15 + 25 = 40 the answer is d ."
Answer: d
Python program:
a = 10 + 14 
b = a + 14
Problem: a ’ s speed is 51 / 44 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 / 51 , b ) 4 / 51 , c ) 7 / 51 , d ) 3 / 44 , e ) 7 / 44
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 51 meters , b covers 44 meters in that time . so if the race is 51 meters long , when a reaches the finish line , b would be 7 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 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 51 meters ) would be the same as the time required by b ( to cover 44 meters ) to reach the finish line . so b should get a head start of 7 / 51 th of the race . answer ( c )"
Answer: c
Python program:
a = 51 - 44
b = a / 51
Problem: john and mike enter into a partnership by investing $ 700 and $ 300 respectively . at the end of one year , they divided their profits such that a third of the profit is divided equally for the efforts they have put into the business and the remaining amount of profit is divided in the ratio of the investments they made in the business . if john received $ 800 more than mike did , what was the profit made by their business in that year ?
Options: a ) 46457 , b ) 465745 , c ) 3000 , d ) 3456 , e ) 35346
Rationale: say the profit was $ x . john share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.7 mike ' s share = x / 6 ( half of the third ) + ( x - x / 3 ) * 0.3 thus ( x - x / 3 ) * 0.7 - ( x - x / 3 ) * 0.3 = 800 - - > x = 3000 . answer is c
Answer: c
Python program:
a = 2 / 3
b = 700 + 300 
c = 700 / b
d = a * c
e = 2 / 3
f = 700 + 300 
g = 300 / f
h = e * g
i = d - h
j = 800 / i
Problem: two men are walking towards each other alongside a railway track . a freight train overtakes one of them in 20 seconds and exactly 10 minutes later meets the other man coming from the opposite direction . the train passes this man is 18 seconds . assume the velocities are constant throughout . how long after the train has passed the second man will the two men meet ?
Options: a ) 89.7 minutes , b ) 90 minutes , c ) 90.3 seconds , d ) 91 seconds , e ) none of these
Rationale: explanation : let ‘ l ’ be the length of train , ‘ x ’ be the speed of the first man , ‘ y ’ be the speed of the second man and ‘ z ’ be the speed of the train . = > 20 = 1 / ( z − x ) and = > 18 = 1 / ( z + x ) = > z = 10 x + 9 y . distance between the two men = 600 ( z + y ) . time = ( 600 ( z + y ) - 600 ( x + y ) ) / ( x + y ) . = > 600 ( 9 x + 9 y ) / ( x + y ) . = > 90 minutes . answer : b
Answer: b
Python program:
a = const_60 * 10
b = 18 / 2
c = a * b
d = c / const_60
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 16 % , then the cost price of the article is :
Options: a ) 500 , b ) 334 , c ) 531 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 116 = rs . 531 answer : option c"
Answer: c
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 16 
g = e / f
Problem: a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is :
Options: a ) 2 , b ) 5 , c ) 9 , d ) 7 , e ) 6
Rationale: let the number be x x - 4 = 21 / x x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 correct answer d
Answer: d
Python program:
a = 4 * 21
b = 4 ** 2
c = a + b 
d = math.sqrt(c)
e = d + 4 
f = e / 2
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3520 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 440 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3520 × ( 1 / 8 ) = 440 answer : option d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 3 * e
g = f * 3520
Problem: a is half good a work man as b and together they finish a job in 15 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 45 / 2 , d ) 36 , e ) 48
Rationale: "c 45 / 2 wc = 1 : 2 2 x + x = 1 / 15 = > x = 1 / 45 2 x = 2 / 45 = > 45 / 2 days"
Answer: c
Python program:
a = 3 / 2
b = 15 * a
Problem: bookman purchased 30 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 240 , how many paperback copies were sold ?
Options: a ) 8 , b ) 12 , c ) 6 , d ) 4 , e ) 5
Rationale: "the bookman had 10 hardback ad 30 - 10 = 20 paperback copies ; 14 copies were sold , hence 30 - 14 = 16 copies were left . let # of paperback copies left be p then 10 p + 20 ( 16 - p ) = 240 - - > 10 p = 80 - - > p = 8 # of paperback copies sold is 20 - 8 = 12 answer : b"
Answer: b
Python program:
a = 30 - 10
b = a * 10
c = 10 * 20
d = b + c 
e = d - 240
f = math.gcd(30, 10)
g = f * 20
h = e - g
i = h / 10
Problem: a train running at the speed of 80 km / hr crosses a pole in 10 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 350 m , c ) 150 m , d ) 250 m , e ) 240 m
Rationale: speed = ( 90 * 5 / 18 ) m / sec = 25 m / sec length of the train = ( speed x time ) = ( 25 * 10 ) m = 250 m . answer : d
Answer: d
Python program:
a = 80 * 1000
b = a / 3600
c = b * 10
Problem: a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ' s share is :
Options: a ) 240 , b ) 120 , c ) 280 , d ) 160 , e ) 200
Rationale: "let c ' s share = rs . x then , b ' s share = rs . x / 4 , a ' s share = rs . ( 2 / 3 x ( x / 4 ) ) = rs . x / 6 therefore , x / 6 + x / 4 + x = 1360 = 17 x / 12 = 1360 x = 1360 x 12 / 17 = rs . 960 hence , b ' s share = rs . ( 960 / 4 ) = rs . 240 . answer is a ."
Answer: a
Python program:
a = 1360 / 10
b = a * 2
c = b - 12
d = c - 12