Practice Quantitative Aptitude questions on Chain Rule, covering direct and inverse proportions, relationships between multiple quantities, and calculations involving workers, time, wages, machines, and production rates. This practice test helps students solve multi-step proportionality problems for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
34 men can complete a piece of work in 18 days. In how many days will 17 men complete the same work?
Explanation
Work is proportional to men x days. 34 × 18 = 17 x d, so d = 36 days. Fewer men need proportionally more days.
Question 2
Hiralal wants to build a tank. He employed 7 workers to do the work. It was expected to get completed in 12 days. 5 days after starting the work, 2 workers were fired by him. Remaining workers will take how much time to complete the work?
Explanation
The total work = 7 × 12 = 84 worker-days. In 5 days, 7 × 5 = 35 worker-days are done, leaving 49 worker-days.
5 workers remain, so the time = 495 days.
5 workers remain, so the time = 495 days.
Question 3
54 toymakers can prepare 36 toys per day. Ajay wants 416 toys. How many toymakers should he employ to get the job done in 16 days?
Explanation
54 toymakers make 36 toys per day, so each toymaker makes 23 toy per day.
He needs 416 toys in 16 days, that is 26 toys per day.
Toymakers needed = 26 ÷ 23 = 39.
He needs 416 toys in 16 days, that is 26 toys per day.
Toymakers needed = 26 ÷ 23 = 39.
Question 4
40 boys working 9 hours per day paint a house in 96 days. How many hours per day 48 boys need to work so they can paint the house in 45 days?
Explanation
The work = 40 × 9 × 96 = 34,560 boy-hours.
48 boys working for 45 days at h hours a day: 48 × 45 × h = 34,560, so h = 345602160 = 16 hours.
48 boys working for 45 days at h hours a day: 48 × 45 × h = 34,560, so h = 345602160 = 16 hours.
Question 5
If 36 men can do a piece of work in 25 hours, in how many hours will 10 men do it?
Explanation
The work = 36 × 25 = 900 man-hours.
10 men take 90010 = 90 hours.
10 men take 90010 = 90 hours.
Question 6
If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12 days, then find the number of days the same number of people will require to dig earth 75m deep, 20m long and 50m broad.
Explanation
The volume of earth dug in the first case = 100 × 25 × 30 = 75,000 cubic metres, and in the second case = 75 × 20 × 50 = 75,000 cubic metres.
The volumes are equal, so the same number of people need the same 12 days.
The volumes are equal, so the same number of people need the same 12 days.
Question 7
If a cloth merchant sells ‘a’ metres of cloth for Rs.x, then what is the selling price of ‘b’ metres of cloth?
Explanation
The price of 'a' metres is Rs. x, so the price of 1 metre = Rs. xa.
The price of 'b' metres = Rs. b × xa.
The price of 'b' metres = Rs. b × xa.
Question 8
A contractor undertakes to renew a road within 30 days and immediately employs 24 men. At the end of 21 days the work is only half done. How many more men should he employ to complete the work in time?
Explanation
24 men have done half the work in 21 days, so the other half must be done in the remaining 9 days.
The work done by 24 men in 21 days = 24 × 21 = 504 man-days for half of the work, so 504 man-days are needed for the rest in 9 days.
Men required = 5049 = 56, so the additional men = 56 - 24 = 32.
The work done by 24 men in 21 days = 24 × 21 = 504 man-days for half of the work, so 504 man-days are needed for the rest in 9 days.
Men required = 5049 = 56, so the additional men = 56 - 24 = 32.
Question 9
If 6 horses eat 108 kg wheat in 4 days, how much wheat is needed for 20 horses for 3 days?
Explanation
6 horses eat 108 kg in 4 days, so 1 horse eats 1086 × 4 = 4.5 kg per day.
20 horses for 3 days eat 20 × 3 × 4.5 = 270 kg.
20 horses for 3 days eat 20 × 3 × 4.5 = 270 kg.
Question 10
A garrison has ration for 80 soldiers to last for 60 days. For how many more days will the remaining ration last if 20 additional soldiers join them after 15 days?
Explanation
The ration for 80 soldiers for 60 days = 4800 man-days. After 15 days, 80 × 15 = 1200 man-days are used, leaving 3600 man-days.
With 100 soldiers the remaining ration lasts 3600100 = 36 days.
With 100 soldiers the remaining ration lasts 3600100 = 36 days.
Question 11
If 10 men weave 10 mats in 10 days, how many men will be required to weave 100 mats in 100 days?
Explanation
10 men weave 10 mats in 10 days, so 1 man weaves 1 mat in 10 days.
100 mats in 100 days means 1 mat per day, and each man weaves 110 of a mat per day, so the men required = 1110 = 10.
100 mats in 100 days means 1 mat per day, and each man weaves 110 of a mat per day, so the men required = 1110 = 10.
Question 12
Rs. 1105 is spent on food of 12 men for 17 days. For how many persons will Rs. 1170 be spent on food for 27 days?
Explanation
Rs. 1105 feeds 12 men for 17 days = 204 man-days, so the cost per man-day = 1105204.
For Rs. 1170 over 27 days: the number of men = 1170 × 2041105 × 27 = 8.
For Rs. 1170 over 27 days: the number of men = 1170 × 2041105 × 27 = 8.
Question 13
4500 men have provisions for 15 days at a rate of 390 gm/head/day. How many men must leave so that food may last for 27 days when the ratio is reduced to 300 gm/head/day?
Explanation
The total food = 4500 men × 15 days × 390 gm = 4500 × 15 × 390 gm.
Let n men remain: n × 27 × 300 = 4500 × 15 × 390, so n = 4500 × 15 × 39027 × 300 = 3250.
Men who must leave = 4500 - 3250 = 1250.
Let n men remain: n × 27 × 300 = 4500 × 15 × 390, so n = 4500 × 15 × 39027 × 300 = 3250.
Men who must leave = 4500 - 3250 = 1250.
Question 14
A five day cricket match is played for 30 hours, the duration of the play being the same every day. If a match stops after 3 days due to rain, find for how many hours the match was played ?
Explanation
The match is played for 30 hours in 5 days, so the duration of play per day = 305 = 6 hours.
In 3 days the match is played for 3 × 6 = 18 hours.
In 3 days the match is played for 3 × 6 = 18 hours.
Question 15
If 90 men can do 90 jobs in 90 days, then 1 man can do one job in :
Explanation
90 men can do 90 jobs in 90 days, so 1 man can do 1 job in 90 days (the men and the jobs are in the same proportion).
Question 16
In a poultry farm, 10 hens eat 10 kg of grain in 10 days. In how many days will one hen eat 1 kg of grain?
Explanation
10 hens eat 10 kg in 10 days, so 1 hen eats 1010 = 1 kg in 10 days.
Question 17
12 men can dig a trench in 36 days working 10 hrs/day. How many hours a day will be required of 36 men working for 30 days to dig that trench?
Explanation
12 × 36 × 10 = 4320 man-day-hours. 36 × 30xh=4320 gives h=4.
Question 18
4 waiters can serve 250 dishes in 8 days by working 5 hours/day. For how many hours/day would 2 waiters have to work to serve 500 dishes in 20 days?
Explanation
4 × 8 × 5=160 waiter-hours serve 250 dishes, a rate of 250160 dishes per waiter-hour. 500 dishes need 320 waiter-hours; with 2 waiters over 20 days that is 320/(2 × 20)=8 hours/day.
Question 19
If 18 binders bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days?
Explanation
Rate = 900/(18 × 10)=5 books per binder-day. For 660 books in 12 days: binder-days=6605=132, binders=13212=11.
Question 20
3 pumps work for 8 hours a day and empty a tank in 2 days. How many hours should 4 pumps work in a day to empty the tank in just 1 day?
Explanation
Total pump-hours = 3 × 8 × 2=48. For 4 pumps in 1 day: hours = 484 = 12.
Question 21
4 painters make 4 paintings in 4 days. At the same rate, how many paintings will be made by 8 painters in 8 days?
Explanation
Rate = 1 painting per 4 painter-days. For 8 painters x 8 days = 64 painter-days: 644 = 16 paintings.
Question 22
In a poultry farm, 30 hens eat 30 bags of grain in 30 days. In how many days will 1 hen eat 1 bag of grain?
Explanation
This is a self-similar scaling: 30 hens eat 30 bags in 30 days means each hen eats 1 bag in 30 days, so 1 hen also eats 1 bag in 30 days.
Question 23
If 13 men can reap a field in 7 days, then 7 men will reap the same field in
Explanation
Men and days are inversely proportional: days = (13 × 7)/7 = 13 days.
Question 24
If 45 toys cost Rs. 157.5, what do 35 toys cost?
Explanation
Rate = 157.545 = 3.5 Rs/toy. Cost of 35 toys = 35 × 3.5 = 122.5.
Question 25
A rope makes 35 rounds of the circumference of a circle whose radius is 28 cm. How many times can it go round with radius 49 cm?
Explanation
Since the rope length is fixed and circumference is proportional to radius, rounds1 x r1 = rounds2 x r2: 35 × 28 = rounds2 × 49, giving rounds2 = 20.
