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

Raman alone can complete a job in 16 days. Frank alone can complete the same job in 24 days. Raman, Frank and Ricky together complete the job in 8 days and get paid a total of Rs. 4000 for it. Find Raman's share (in Rs.).

  1. 2000

  2. 1000

  3. 4000

  4. 1333.33
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Raman's rate = 1/16, Frank's rate = 1/24. Combined rate of Raman and Frank = 1/16 + 1/24 = 5/48. Together with Ricky, they complete the job in 8 days (rate = 1/8). Ricky's rate = 1/8 - 5/48 = 1/48. The work done by each in 8 days: Raman = 8/16 = 1/2, Frank = 8/24 = 1/3, Ricky = 8/48 = 1/6. Raman's share = (1/2) * 4000 = 2000.

Multiple choice

Aman takes 8 days to complete a task. Balkrishan takes 16 days and Chetan takes 24 days to complete the same task. Aman works on the first day and then leaves. Then, Balkrishan and Chetan start working on the task. Balkrishan leaves four days before the task is completed and Chetan is left to complete it. How long will they take to complete the task?

  1. 6.8 days

  2. 7.8 days

  3. 11.8 days

  4. 13.8 days

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = 48 units. Rates: A=6, B=3, C=2. Day 1: A works (6 units). Remaining = 42. Let total time be T. B and C work for T-1 days. B leaves 4 days before end, so B works for T-5 days. C works for T-1 days. 3(T-5) + 2(T-1) = 42. 3T - 15 + 2T - 2 = 42. 5T = 59. T = 11.8.

Multiple choice

A can do a piece of work in 20 days and B can do same work in 30 days. They started the work together but after 9 days A left the job. In how many days B will complete the rest of the work

  1. 7 1/2 days

  2. 12 1/2 days

  3. 15

  4. 20

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

A and B together do (1/20 + 1/30) = 5/60 = 1/12 of the work per day. In 9 days, they complete 9/12 = 3/4 of the work, leaving 1/4 of the work for B. Since B completes 1/30 of the work per day, B takes (1/4) / (1/30) = 30/4 = 7.5 days.

Multiple choice

X and Y together finish a piece of work in 30 days. X works for 16 days and Y finishes the remaining work alone in 44 days. In how many days will Y finish the whole work?

  1. 60 days

  2. 46 days

  3. 14 days

  4. 28 days

  5. 37 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let X and Y be the work rates. We have 30(X+Y) = 1, so X+Y = 1/30. Also, 16X + 44Y = 1. Substituting X = 1/30 - Y into the second equation gives 16(1/30 - Y) + 44Y = 1, which simplifies to 16/30 + 28Y = 1, or 28Y = 14/30 = 7/15. Thus Y = 7/(15*28) = 1/60. Y takes 60 days.