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: Select the correct alternative from the given choices. A team of N persons can complete a certain job in 15 days. If there were six more persons in the team, it would take three days less to complete the job. Find N.

  1. 24

  2. 30

  3. 18

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the number of persons be N and days be 15. The total work is 15N. If there are N+6 persons, the time taken is 12 days, so the work is 12(N+6). Setting 15N = 12N + 72, we get 3N = 72, so N = 24.

Multiple choice

Directions: Select the correct alternative from the given choices. A contractor observed that with the existing number of workers, he could finish a project in 12 days. However, if he added 20 more workers to the existing team, the project will be completed in 10 days. How many days would a single worker take to complete the entire project?

  1. 480

  2. 600

  3. 800

  4. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let x be the number of workers. Work = x * 12. Also Work = (x+20) * 10. 12x = 10x + 200, 2x = 200, x = 100. Total work = 100 * 12 = 1200 worker-days.

Multiple choice

Directions: Type in your answer in the input box provided below the question. A starts a certain work and after he completes exactly half the work, he leaves and B takes up the remaining work and it takes a total of 25 days for the work to be completed this way. If A and B working together can complete the work in 12 days, and A is slower than B, then find the number of days in which the work will be completed, if A alone first works on exactly one-fifth of the work, after which B alone completes the rest of the work.

  1. 21

  2. 22

  3. 23

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A and B take 'a' and 'b' days to complete the work. 1/a + 1/b = 1/12. Given 0.5a + 0.5b = 25, so a + b = 50. Solving the system: x^2 - 50x + 600 = 0, giving roots 20 and 30. Since A is slower, A=30, B=20. For the second scenario: (1/5) * 30 + (4/5) * 20 = 6 + 16 = 22 days.

Multiple choice

To do a certain work, the ratio of efficiencies of A and B is 3 : 7. Working together, they can complete a work in 14 days. B started the work and after working for 8 days, he left and A completed the remaining work. For how many days did A work?

  1. 28

  2. 30

  3. 24

  4. 27
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let efficiencies be 3x and 7x. Total work = (3x + 7x) * 14 = 140x. B works for 8 days, completing 7x * 8 = 56x. Remaining work is 140x - 56x = 84x. A completes this at 3x efficiency, taking 84x / 3x = 28 days.

Multiple choice

A can do a piece of work in 20 days, B can do the same piece of work in 30 days. A and B start working together and after working for 10 days, A leaves and B has to complete the remaining work himself. If A was given $550 for the work done by him, what amount of money will B get?
  1. $300
  2. $380
  3. $440
  4. $550
  5. $600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's work rate = 1/20, B's = 1/30. In 10 days, A does 10/20 = 1/2 of work. B does 10/30 = 1/3 of work. Total work done by both = 1/2 + 1/3 = 5/6. Remaining work = 1/6, done by B. Total work by B = 1/3 + 1/6 = 1/2. Since A and B did equal amounts of work (1/2 each), they should get equal pay. A got 550, so B gets 550.

Multiple choice

A contractor has two teams of workers, team A and team B. Team A can complete a project P in 12 days and team B can complete it in 36 days. Team A starts working on P and team B joins team A after four days. Team A is withdrawn after another two days and team B is asked to double its efficiency. The number of additional days required for team B to complete P is

  1. 6

  2. 8

  3. 15

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Team A rate = 1/12, Team B rate = 1/36. In 4 days, A does 4/12 = 1/3. In next 2 days, A+B do 2(1/12 + 1/36) = 2(4/36) = 2/9. Total done = 1/3 + 2/9 = 5/9. Remaining = 4/9. B's new rate = 2/36 = 1/18. Time = (4/9) / (1/18) = 8 days.