euclaise/mathqa_programs huggingface dataset:
Problem: a mixture contains milk and water in the ratio 3 : 2 . on adding 10 litters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?
Options: a ) 10 , b ) 30 , c ) 50 , d ) 20 , e ) 30
Rationale: "explanation : milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 milk parts always same short cut method : milk : water = 6 : 4 after adding 10 liters of water milk : water = 6 : 9 milk is same but water increse 10 liters then the water ratio is increse 5 parts 5 part - - - - - > 10 liters the quantity of milk in the original mixture is = 6 : 4 = 6 + 4 = 10 10 parts - - - - - > 20 liters ( answer is = 20 ) short cut method - 2 : for only milk problems milk : water 6 : 4 6 : 9 milk ratio same but water ratio 5 parts incress per 10 liters 5 part of ratio - - - - - - - > 10 liters 10 part of ratio - - - - - - > 20 liters answer : option d"
Answer: d
Python program:
a = 2 / 3
b = 10 * a
c = 3 + 2 
d = 3 / c
e = 3 + 2 
f = 2 / e
g = 2 / 3
h = f * g
i = d - h
j = b / i
Problem: a drink vendor has 80 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 35 , b ) 37 , c ) 42 , d ) 30 , e ) 38
Rationale: "the number of liters in each can = hcf of 80 , 144 and 368 = 16 liters . number of cans of maaza = 80 / 16 = 5 number of cans of pepsi = 144 / 16 = 9 number of cans of sprite = 368 / 16 = 23 the total number of cans required = 5 + 9 + 23 = 37 cans . answer : b"
Answer: b
Python program:
a = math.gcd(80, 144)
b = math.gcd(a, 368)
c = 368 / b
d = math.gcd(80, 144)
e = math.gcd(d, 368)
f = 80 / e
g = math.gcd(80, 144)
h = math.gcd(g, 368)
i = 144 / h
j = f + i 
k = c + j
Problem: ( 112 % of 2348 ) ÷ 4.98 = ?
Options: a ) 505 , b ) 515 , c ) 525 , d ) 538 , e ) 567
Rationale: "explanation : ? = ( 112 x 2348 / 100 ) ÷ 5 = 2630 / 5 = 526 = 525 answer : option c"
Answer: c
Python program:
a = 112 / 100
b = a * 2348
c = b / 4
Problem: the unit digit in the product 1256 * 6785 * 4587 * 9785 is ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 6 * 5 * 7 * 5 = 0 answer is a"
Answer: a
Python program:
a = 1256 * 6785
b = a * 4587
c = b * 9785
d = 1256 * 6785
e = d * 4587
f = e * 9785
g = 4 + 4 
h = f - g
i = c - h
Problem: a man can row upstream at 60 kmph and downstream at 90 kmph , and then find the speed of the man in still water ?
Options: a ) 75 kmph , b ) 65 kmph , c ) 30 kmph , d ) 73 kmph , e ) 65 kmph
Rationale: us = 60 ds = 90 m = ( 60 + 90 ) / 2 = 75 answer : a
Answer: a
Python program:
a = 60 + 90 
b = a / 2
Problem: a train running at the speed of 52 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 130 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 440 m
Rationale: "speed = 52 * 5 / 18 = 130 / 9 m / sec length of the train = speed * time = 130 / 9 * 9 = 130 m answer : a"
Answer: a
Python program:
a = 52 * 1000
b = a / 3600
c = b * 9
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 441 in 2 years ?
Options: a ) 387 , b ) 400 , c ) 776 , d ) 268 , e ) 181
Rationale: "441 = p ( 21 / 20 ) 2 p = 400 answer : b"
Answer: b
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 441 / c
Problem: solve the quickfire maths brain teaser â ˆ š 36 % = ?
Options: a ) 30 % , b ) 40 % , c ) 60 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 36 % = > â ˆ š 36 / â ˆ š 100 = > 6 / 10 = > 60 / 100 = > 60 % c"
Answer: c
Python program:
a = 1 + 36 
b = 100 / a
Problem: a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 900 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 10000 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 12012
Rationale: "[ 900 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 10000 answer : a"
Answer: a
Python program:
a = 5 / 100
b = 600 / a
Problem: jaime earned enough money by selling seashells at 30 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 22 , c ) 17 , d ) 25 , e ) 30
Rationale: "let ' s test answer b : 22 seashells . . . with 22 seashells , jamie would have 22 ( 30 ) = 660 cents . this would allow him to buy 12 books for 660 cents total , with no money left over . this is an exact match for what we were told , so this must be the answer . final answer : [ reveal ] spoiler : b"
Answer: b
Python program:
a = math.lcm(30, 55)
b = a / 30
c = b + 10
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 180 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.7 gallons , d ) 4.5 gallons , e ) 7.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 180 ÷ 40 = 4.5 × 1 gallon = 4.5 gallons correct answer is d ) 4.5 gallons"
Answer: d
Python program:
a = 180 / 40
Problem: what is the area of a square field whose diagonal of length 18 m ?
Options: a ) 120 sq m , b ) 250 sq m , c ) 200 sq m , d ) 180 sq m , e ) 100 sq m
Rationale: "d 2 / 2 = ( 18 * 18 ) / 2 = 180 answer : d"
Answer: d
Python program:
a = square_area / (
Problem: a car covers a distance of 624 km in 3 1 / 5 hours . find its speed ?
Options: a ) 104 kmph , b ) 195 kmph , c ) 109 kmph , d ) 174 kmph , e ) 101 kmph
Rationale: "624 / 3 1 / 5 = 195 kmph answer : b"
Answer: b
Python program:
a = 1 / 5
b = 3 + a 
c = 624 / b
Problem: a train which has 400 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 40 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 400 / ( ( 45 - 9 ) ( 5 / 18 ) = 400 / 36 * ( 5 / 18 ) = 400 / 10 = 40 sec answer : b"
Answer: b
Python program:
a = 45 / const_3_6
b = 9 / 2
c = b / const_3_6
d = a - c
e = 400 / d
Problem: if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 5 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: "for n ( n + 1 ) to be a multiple of 5 , either n or n + 1 has to be a multiple of 5 . thus n must be of the form 5 k or 5 k - 1 . the probability is 2 / 5 . the answer is e ."
Answer: e
Python program:
a = 2 / 5
Problem: each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a odd number written on it ?
Options: a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9
Rationale: "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d"
Answer: d
Python program:
a = 4 + 1 
b = 9 + 1 
c = a / b
d = 4 + 1 
e = d - 1
f = 9 + 1 
g = f - 1
h = e / g
i = c * h
j = 4 + 1 
k = j - 1
l = k - 1
m = 9 + 1 
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 4 + 1 
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1 
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z
Problem: a superhero flies at an incredible rate of 1000 kilometers per minute . what is her speed in miles per hour ? [ 1 km = 0.6 miles ]
Options: a ) 6000 , b ) 36000 , c ) 60000 , d ) 600 , e ) 3600
Rationale: to calculate the equivalent of miles in a kilometer 0.6 kilometers = 1 mile 1000 kilometers = ( 0.6 ) * 1000 = 600 miles speed in miles per minute = 600 = 600 1 hour = 60 minutes speed in miles per hour = 600 * 60 = 36,000 correct answer - b
Answer: b
Python program:
a = 1000 * const_60
b = a * 0
Problem: 5100 − ( 102 ÷ 20.4 ) = ?
Options: a ) 5200 , b ) 5150 , c ) 5250 , d ) 6150 , e ) 5095
Rationale: explanation : = 5100 − ( 102 / 204 × 10 ) = 5100 − 5 = 5095 option e
Answer: e
Python program:
a = 102 / 20
b = 5100 - a
Problem: in a sports club with 30 members , 17 play badminton and 21 play tennis and 2 do not play either . how many members play both badminton and tennis ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let x play both badminton and tennis so 17 - x play only badminton and 19 - x play only tennis . 2 play none and there are total 30 students . hence , ( 17 - x ) + ( 21 - x ) + x + 2 = 30 40 - 2 x + x = 30 40 - x = 30 x = 10 so 10 members play both badminton and tennis . d"
Answer: d
Python program:
a = 17 + 21 
b = a + 2 
c = b - 30
Problem: in 40 litres of a mixture , the ratio of milk to water is 7 : 1 . in order to make the ratio of milk to water as 3 : 1 , the quantity of water that should be added to the mixture will be ?
Options: a ) rs . 1000 , b ) rs . 1200 , c ) rs . 1400 , d ) rs . 1600 , e ) rs . 2500
Rationale: explanation : total simple interest received , i = rs . 1600 principal , p = 7000 period , n = 5 years rate of interest , r = ? simple interest , i = p n r 100 i = pnr 100 ⇒ 1600 = 7000 × 5 × r 100 ⇒ r = 1600 × 100 7000 × 5 = 160 35 = 32 7 % ⇒ 1600 = 7000 × 5 × r 100 ⇒ r = 1600 × 1007000 × 5 = 16035 = 327 % by rule of alligation , rate of interest % from part 1 rate of interest % from part 2 6 4 net rate of interest % 32 7 327 32 7 − 4 = 4 7 327 − 4 = 47 6 − 32 7 = 10 7 6 − 327 = 107 = > part 1 : part 2 = 4 7 : 10 7 = 4 : 10 = 2 : 5 = 47 : 107 = 4 : 10 = 2 : 5 given that total amount is rs . 7000 . therefore , the amount lent at 6 % per annum ( part 1 amount ) = 7000 × 2 7 = rs . 2000 d )
Answer: d
Python program:
a = 3 / 1
b = 7 / 1
c = a * b
d = c * 40
e = d * 2
f = 40 * 2
g = e - f
Problem: 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 388 , b ) 266 , c ) 350 , d ) 112 , e ) 134
Rationale: speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 39 = 50 / 3 3 ( x + 300 ) = 1950 è x = 350 m . answer : c
Answer: c
Python program:
a = speed * (
b = a - 39
Problem: a person want to give his money of $ 12000 to his 5 children a , b , c , d , e in the ratio 2 : 4 : 3 : 1 : 5 . what is the d + e share ?
Options: a ) $ 1800 , b ) $ 2800 , c ) $ 3800 , d ) $ 5800 , e ) $ 4800
Rationale: "d ' s share = 12000 * 1 / 15 = $ 800 d ' s share = 12000 * 5 / 15 = $ 4000 a + d = $ 4800 answer is e"
Answer: e
Python program:
a = 2 + 0 
b = a + 3 
c = 5 / b
d = c * 12000
Problem: an enterprising businessman earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just double of that made on the previous day . on the 20 th day of business , he earns an income of :
Options: a ) rs 219 , b ) rs 220 , c ) rs 20 ² , d ) rs 20 , e ) rs 30
Rationale: "2 nd day he earns = 2 = 2 ( 2 – 1 ) 3 rd day he earns = 2 ( 3 – 1 ) on 20 th day he earns 2 ( 20 - 1 ) = 219 rupees answer : a"
Answer: a
Python program:
a = 1 * 20
b = a - 1
Problem: two cars started from the same point , at 5 am , traveling in opposite directions at 40 and 50 mph respectively . at what time will they be 450 miles apart ?
Options: a ) 8 am , b ) 10 am , c ) 11 am , d ) 12 am , e ) 14 am
Rationale: after t hours the distances d 1 and d 2 , in miles per hour , traveled by the two cars are given by d 1 = 40 t and d 2 = 50 t after t hours the distance d separating the two cars is given by d = d 1 + d 2 = 40 t + 50 t = 90 t distance d will be equal to 450 miles when d = 90 t = 450 miles t = 5 hours . 5 am + 5 hours = 10 am answer : b
Answer: b
Python program:
a = 40 + 50 
b = 450 / a
c = b + 5
Problem: if 8 men or 12 women can do a piece of work in 20 days , in how many days can the same work be done by 6 men and 11 women ?
Options: a ) 10 days , b ) 11 days , c ) 12 days , d ) 15 days , e ) 17 days
Rationale: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 20 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 20 = 1 / 240 so , 20 women work = 20 / 240 = 1 / 12 ans : 12 days answer : c"
Answer: c
Python program:
a = 8 * 20
b = 6 / a
c = 12 * 20
d = 11 / c
e = b + d 
f = 1/(e)
Problem: 3 men can complete a piece of work in 6 days . two days after they started the work , 3 more men joined them . how many days will they take to complete the remaining work ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : 3 man 1 day work = 1616 3 man 2 days work = 2626 remaining work = ( 1 – 2626 ) = 2 / 3 parts . 6 man together perform the work in 1 day is = 1616 + 1616 = 2626 parts 2626 parts completed in 1 day 2323 parts will b completed in 2 days answer : a
Answer: a
Python program:
a = 2 / 6
b = 1 - a
c = 3 * 6
d = b * c
e = d / 6
Problem: 36 people { a 1 , a 2 … a 36 } meet and shake hands in a circular fashion . in other words , there are totally 36 handshakes involving the pairs , { a 1 , a 2 } , { a 2 , a 3 } , … , { a 35 , a 36 } , { a 36 , a 1 } . then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
Options: a ) 76
b ) 55
c ) 44
d ) 12
e ) 91
Rationale: ans : { a 1 , a 2 } , { a 2 , a 3 } , { a 3 , a 4 } , { a 4 , a 5 } , { a 5 , a 6 } , { a 6 , a 7 } … , { a 35 , a 36 } , { a 36 , a 1 } from the above arrangement , if we separate a 3 , a 6 , a 9 , . . . . . a 36 . total 12 persons the reamining persons must have shaked hand with atleast one person . so answer is 12 . answer : d
Answer: d
Python program:
a = 36 / 3
Problem: rates for having a manuscript typed at a certain typing service are $ 6 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 35 were revised only once , 15 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 860 , b ) $ 850 , c ) $ 840 , d ) $ 830 , e ) $ 820
Rationale: "50 pages typed 1 x 35 pages typed 2 x ( original + one revision ) 15 pages typed 3 x ( original + two revisions ) 50 ( 6 ) + 35 ( 6 + 4 ) + 15 ( 6 + 4 + 4 ) = 300 + 350 + 210 = 860 answer - a"
Answer: a
Python program:
a = 100 * 6
b = 35 * 4
c = a + b 
d = 15 * 4
e = d * 2
f = c + e
Problem: the perimeter of a semi circle is 216 cm then the radius is ?
Options: a ) 26 , b ) 48 , c ) 98 , d ) 37 , e ) 42
Rationale: "36 / 7 r = 216 = > r = 42 answer : e"
Answer: e
Python program:
a = 2 + math.pi 
b = 216 / a
Problem: a train 360 metre long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 metre long ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: speed = 45 km / hr = 45 × 5 / 18 = 25 / 2 m / s distance travelled = ( speed x time ) time = ( distance travelled / speed ) distance travelled = length of the train + length of the platform = 360 + 140 = 500 m = 500 / 25 / 2 = 40 sec answer : c
Answer: c
Python program:
a = 360 + 140 
b = a / 1000
c = b / 45
d = c * 3600
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 18 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 12 / 112 , b ) 6 / 81 , c ) 11 / 61 , d ) 12 / 33 , e ) 3 / 19
Rationale: "let us say probability of a occuring is a . let us say probability of b occuring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 18 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 18 * 2 b * b 3 b - 2 b ^ 2 = 36 b ^ 2 3 b = 38 b ^ 2 b = 3 / 38 so , a = 2 b = 6 / 38 = 3 / 19 the correct answer is e ."
Answer: e
Python program:
a = 2 + 1 
b = 18 * 2
c = b + 2 
d = a / c
e = d * 2
Problem: a student got twice as many sums wrong as he got right . if he attempted 24 sums in all , how many did he solve correctly ?
Options: a ) 12 , b ) 16 , c ) 8 , d ) 24 , e ) 26
Rationale: explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 24 3 x = 24 x = 8 . answer : c
Answer: c
Python program:
a = 1 + 2 
b = 24 / a
Problem: a 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 277 , e ) 400
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 42 = 50 / 3 3 x + 900 = 2200 = > x = 400 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 42
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 10 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 54 % , b ) 70 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( 1.1 ) , which is 1.54 and a 54 % increase . a"
Answer: a
Python program:
a = 40 / 100
b = 1 + a 
c = 100 * b
d = 10 / 100
e = 1 + d 
f = c * e
g = f / 100
h = g - 1
i = h * 100
Problem: the time it took car p to travel 900 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 40 , b ) 54 , c ) 62 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 900 / x ) - ( 900 / ( x + 10 ) ) = 2 solving for x = 62 miles \ hr . c"
Answer: c
Python program:
a = negate + ( 
b = negate ** (
c = b - 2
d = 900 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
Problem: how many seconds will a 400 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 24 , e ) 60
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 400 * 3 / 50 = 24 sec . answer : option d"
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 400 / b
Problem: a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: "let c = revenue from car sales in 1996 let t = revenue from truck sales in 1996 equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997 , c ( 0.89 ) + t ( 1.07 ) = ( c + t ) ( 1.01 ) dividing throughout by t , ( c / t ) ( 0.89 ) + 1.07 = ( c / t + 1 ) ( 1.01 ) = > ( c / t ) ( 0.12 ) = 0.06 = > ( c / t ) = 1 / 2 option ( a ) ."
Answer: a
Python program:
a = 100 + 1997 
b = 100 + 1997 
c = a - b
d = 100 + 1997 
e = 100 - 11
f = d - e
g = c / f
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 150 more . what was the sum ?
Options: a ) s . 120 , b ) s . 130 , c ) s . 140 , d ) s . 150 , e ) s . 300
Rationale: at 5 % more rate , the increase in s . i for 10 years = rs . 150 ( given ) so , at 5 % more rate , the increase in si for 1 year = 150 / 10 = rs . 15 / - i . e . rs . 15 is 5 % of the invested sum so , 1 % of the invested sum = 15 / 5 therefore , the invested sum = 15 × 100 / 5 = rs . 300 answer : e
Answer: e
Python program:
a = 5 / 100
b = a * 10
c = 150 / b
Problem: 12 men can complete a piece of work in 4 days , while 15 women can complete the same work in 4 days . 6 men start working on the job and after working for 2 days , all of them stopped working . how many women should be put on the job to complete the remaining work , if it so to be completed in 3 days ?
Options: a ) 15 women , b ) 85 women , c ) 75 women , d ) 65 women , e ) 35 women
Rationale: "1 man ' s 1 day work = 1 / 48 ; 1 woman ' s 1 day work = 1 / 60 . 6 men ' s 2 day ' s work = 6 / 48 * 2 = 1 / 4 . remaining work = ( 1 - 1 / 4 ) = 3 / 4 now , 1 / 60 work is done in 1 day by 1 woman . so , 3 / 4 work will be done in 3 days by ( 60 * 3 / 4 * 1 / 3 ) = 15 women . answer : a"
Answer: a
Python program:
a = 1 / 4
b = a / 15
c = 1 / b
d = 6 * 2
e = 1 / 4
f = e / 12
g = d * f
h = 1 - g
i = c * h
j = 1 / 3
k = i * j
Problem: in a stream running at 2 kmph , a motor boat goes 10 km upstream and back again to the starting point in 55 minutes . find the speed of motor boat in still water ?
Options: a ) 11 , b ) 15 , c ) 22 , d ) 18 , e ) 25
Rationale: "let the speed of motor boat instill water be x kmph then , speed in downstream = ( x + 2 ) km and . speed in upstream = ( x - 2 ) kmph time taken to row 10 km & back = ( 10 / x + 2,10 / x - 2 ) 10 / x + 2 + 10 / x - 2 = 55 / 60 11 x 2 - 240 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 or x = - 2 / 11 then x = 22 kmph answer is c ."
Answer: c
Python program:
a = 10 + 10 
b = 55 / const_60
c = a / b
Problem: a train 100 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 19 kmph , b ) 18 kmph , c ) 72 kmph , d ) 17 kmph , e ) 91 kmph
Rationale: "length = speed * time speed = l / t s = 100 / 20 s = 5 m / sec speed = 5 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 18 kmph answer : b"
Answer: b
Python program:
a = 100 / 1000
b = 20 / 3600
c = a / b
Problem: if the sales tax be reduced from 4 ( 1 / 5 ) % to 3 ( 1 / 4 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 5400 ?
Options: a ) rs . 100.2 , b ) rs . 50.2 , c ) rs . 20.5 , d ) rs . 100 , e ) none of these
Rationale: "explanation : required difference = ( 4 ( 1 / 5 ) of rs . 5400 ) - ( 3 ( 1 / 4 ) of rs . 5400 ) = ( 21 / 5 – 13 / 4 ) % of rs . 5400 = ( 19 / 20 ) x ( 1 / 100 ) x 5400 = rs . 51.30 answer e"
Answer: e
Python program:
a = 1 / 4
b = 4 + a 
c = b / 100
d = c + 1 
e = 1 / 4
f = e + 1 
g = f / 100
h = g + 1 
i = 5400 / h
j = d * i
k = j - 5400
Problem: there are 2 sections a and b in a class , consisting of 30 and 20 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?
Options: a ) 35 kg , b ) 37 kg , c ) 42 kg , d ) 38 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 30 * 40 + 20 * 35 = 1900 average weight of the class is = 1900 / 50 = 38 kg answer is d"
Answer: d
Python program:
a = 30 * 40
b = 20 * 35
c = a + b 
d = 30 + 20 
e = c / d
Problem: a person can swim in still water at 6 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 14 km ?
Options: a ) 3.5 , b ) 4.5 , c ) 5 , d ) 9 , e ) 6
Rationale: "m = 6 s = 2 us = 6 - 2 = 4 d = 42 t = 14 / 4 = 3.5 answer : a"
Answer: a
Python program:
a = 6 - 2
b = 14 / a
Problem: two numbers are respectively 12 % and 60 % more than a third number . the percentage that is first of the second is ?
Options: a ) 50 % , b ) 60 % , c ) 70 % , d ) 80 % , e ) 90 %
Rationale: "i ii iii 112 160 100 160 - - - - - - - - - - 112 100 - - - - - - - - - - - ? = > 70 % answer : c"
Answer: c
Python program:
a = 12 + 100 
b = 60 + 100 
c = a / b
d = c * 100
e = 100 - d