Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question. In how many days can John, Ben and Mary complete the work? A. John alone can complete the work in 12 days. B. John and Mary together can complete the work in 4 days. C. Mary and Ben together can complete the work in 5 days.

  1. Both statements A and C

  2. Only statement B

  3. Either statement A or C

  4. Both statements A and B

  5. Any one of them
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A: John = 1/12. B: John + Mary = 1/4. C: Mary + Ben = 1/5. From A and B, Mary = 1/4 - 1/12 = 2/12 = 1/6. From C, Ben = 1/5 - 1/6 = 1/30. Total rate = 1/12 + 1/6 + 1/30 = (5+10+2)/60 = 17/60. Time = 60/17 days. A and C are sufficient.

Multiple choice

3 men, 4 women and 6 boys together can complete a work in 6 days. A woman does triple the work a man does and a boy does half the work a man does. How many women alone will be able to complete this work in 4 days?

  1. 9

  2. 6

  3. 8

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M, W, B be the work done by a man, woman, and boy in one day. Given W=3M and B=0.5M, the group (3M+4W+6B) = (3M + 12M + 3M) = 18M. Total work = 18M * 6 days = 108M. To complete 108M in 4 days, the daily work needed is 27M. Since one woman does 3M, the number of women needed is 27M / 3M = 9.

Multiple choice

In a farm, a landlord has assigned a job to the supervisors and workers. It took 8 days for 4 supervisors and 6 workers to finish the work. 3 supervisors and 7 workers took 10 days to complete the same job. If the landlord assigns 10 workers to complete the work, then find out the number of days they will take to finish it.

  1. 40

  2. 20

  3. 35

  4. 50

  5. 60
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let S be the work of a supervisor and W be the work of a worker per day. From the problem, 8(4S + 6W) = 10(3S + 7W), which simplifies to 32S + 48W = 30S + 70W, or 2S = 22W, meaning S = 11W. Substituting back, the total work is 8(4(11W) + 6W) = 8(50W) = 400W. If 10 workers do the job, they take 400W / 10W = 40 days.

Multiple choice

Ron and Sam together can do a piece of work in 8 days. Both start the work together; but after 3 days, Ron falls ill. Sam alone finishes the remaining work in 15 days. How many days would Ron take to finish the whole work alone?

  1. 10

  2. 11

  3. 12

  4. 15

  5. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ron and Sam do 1/8 of the work per day. In 3 days, they do 3/8 of the work. Remaining work = 5/8. Sam does 5/8 of the work in 15 days, so Sam's rate is (5/8)/15 = 1/24 per day. Ron's rate = (1/8) - (1/24) = 3/24 - 1/24 = 2/24 = 1/12. Ron takes 12 days to finish the work alone.

Multiple choice

A female mason works for 8 hr a day for 6 days to finish a certain job. A male mason finishes the same job in 4 days, working 6 hr a day. How many female masons are required to do the job in the same time as taken by the male mason?

  1. 3

  2. 2

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work = 8 * 6 = 48 female-hours. Male work = 4 * 6 = 24 male-hours. Assuming 1 male = 1 female, 48 units / 24 units = 2. The male finishes in 24 hours, so 48/24 = 2 females are needed.

Multiple choice

The efficiency of A and B is equal, but the efficiency of C is half that of B. C and B started a work and 4 days later, A joined them. If C alone can do the work in 28 days, then in how many more days will the work be completed?

  1. 2 2 5 days

  2. 3 1 5 days

  3. 3 2 5 days

  4. 4 5 days

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

C takes 28 days, so C's efficiency is 1/28 of the work per day. B's efficiency is twice C's, so 2/28 = 1/14. A's efficiency equals B's, so 1/14. Total work is 1. After 4 days, C and B have done 4 * (1/28 + 1/14) = 4 * (3/28) = 3/7. Remaining work is 4/7. A, B, and C together do 1/14 + 1/14 + 1/28 = 5/28 per day. Time taken = (4/7) / (5/28) = (4/7) * (28/5) = 16/5 = 3.2 days.

Multiple choice

Kadil, Piyush and Sachin can do a piece of work, working together, in 2 days. Kadil is 6 times as efficient as Piyush. Piyush takes 5 times the number of days as Sachin takes to do it alone. What will be the difference between the number of days taken by Piyush and Kadil?

  1. 12 days

  2. 20 days

  3. 10 days

  4. 4 days

  5. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Sachin take S days. Piyush takes 5S days. Kadil is 6 times as efficient as Piyush, so Kadil takes (5S)/6 days. Together: 1/S + 1/(5S) + 6/(5S) = 1/2. (5+1+6)/(5S) = 1/2. 12/(5S) = 1/2. 5S = 24, S = 4.8. Piyush = 5 * 4.8 = 24 days. Kadil = 24/6 = 4 days. Difference = 24 - 4 = 20 days.

Multiple choice

16 men can finish a work in 12 days. After they worked for 4 days, some more men joined them and they together completed the remaining work in 4 more days. How many more men joined in?

  1. 8

  2. 16

  3. 32

  4. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 16 * 12 = 192 man-days. Work done in 4 days = 16 * 4 = 64 man-days. Remaining work = 192 - 64 = 128 man-days. Remaining time = 4 days. Men needed = 128 / 4 = 32. Original men = 16. New men joined = 32 - 16 = 16.

Multiple choice

Mr. Partap undertook to do a certain piece of construction work in 15 days. Since 6 of the employed labourers were absent from the very first day, the rest could finish the work in 21 days. The original number of men employed was

  1. 15

  2. 19

  3. 12

  4. 21

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the original number of men. The total work is 15x. With (x-6) men, the work takes 21 days, so 21(x-6) = 15x. Solving this: 21x - 126 = 15x, which gives 6x = 126, so x = 21.