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

Time taken by A to finish a piece of work is twice the time taken B and thrice thetime taken by C. If all three of them work together, it takes them 2 days to complete theentire work. How much work was done by B alone?

  1. 2 days

  2. 6 days

  3. 3 days

  4. 5 days

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

Let time for B be x. Then A = 2x, C = 2x/3. Combined rate: 1/(2x) + 1/x + 3/(2x) = 1/2. (1+2+3)/(2x) = 1/2. 6/(2x) = 1/2. 3/x = 1/2, so x = 6. B takes 6 days.

Multiple choice

A and B can paint a fence in 10 days and 15 days, respectively. They work together for 4 days, and then A leaves. How many more days will it take for B to finish painting the fence?

  1. 5 days

  2. 7 days

  3. 8 days

  4. 9 days

  5. 10 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate is 1/10 and B's rate is 1/15. Together, they work at (1/10 + 1/15) = 1/6 of the fence per day. In 4 days, they complete 4/6 = 2/3 of the fence, leaving 1/3 to be finished by B. Since B paints 1/15 per day, it takes B (1/3) / (1/15) = 5 days to finish.

Multiple choice

Two workers, Sarah and David, are paid \$600 together for completing a task. If Sarah works for 8 days and David works for 6 days, they can complete the task. If Sarah works for 12 days, she alone can complete the task. How should the \$600 be divided between Sarah and David?
  1. $350 and $250
  2. $375 and $225
  3. $400 and $200
  4. $425 and $175
  5. $450 and $150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sarah completes the task in 12 days, so her daily rate is 1/12. In 8 days, Sarah does 8/12 = 2/3 of the work. David does the remaining 1/3 in 6 days, so his daily rate is (1/3) / 6 = 1/18. The payment should be proportional to work done: Sarah does 2/3 and David does 1/3. Thus, Sarah gets 2/3 of 600 = 400 and David gets 1/3 of 600 = 200.

Multiple choice

A, B and C can complete the work in 10 days, 30 days and 15 days respectively. If A and B together is helped on every 2nd day by C, in how many days the work will be completed?

  1. 4 days

  2. 6 days

  3. 7 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate = 1/10, B's rate = 1/30, C's rate = 1/15. Day 1: A+B work = 1/10 + 1/30 = 4/30 = 2/15. Day 2: A+B+C work = 2/15 + 1/15 = 3/15 = 1/5. In 2 days, they complete 2/15 + 3/15 = 5/15 = 1/3 of the work. In 6 days, they complete 3 * (1/3) = 1 full work.

Multiple choice

David and Michael together can finish a job in4 days 19 hrs 12 min. If David works at twothirds Michael's speed, how long does it takeMichael alone to finish the same job?

  1. 12DAYS

  2. 15DAYS

  3. 8DAYS

  4. 17DAYS

  5. 11DAYS
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be Michael's rate. David's rate = 2/3 M. Combined rate = 5/3 M. Total time = 4 days 19 hrs 12 min = 115.2 hours. Total work = (5/3 M) * 115.2 = 192 M. Michael alone takes 192/M = 192 hours = 8 days.

Multiple choice

A team of workers intended to finish a project in 15 days. However, with 15 workers leaving the team every day, the project was eventually completed by the end of the 20th day. How many workers were in the group at the project's outset?

  1. 390

  2. 480

  3. 570

  4. 660

  5. 750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let initial workers be x. Total work = 15x. Work done = x + (x-15) + (x-30) + ... + (x-15*19). This is an arithmetic progression with 20 terms. Sum = (20/2) * [2x + (20-1)*(-15)] = 10 * [2x - 285] = 20x - 2850. Setting 20x - 2850 = 15x, 5x = 2850, x = 570.

Multiple choice

A team consists of three workers: X, Y, and Z. X and Y together can complete a certain task in 15 days, while Y and Z together can complete the same task in 20 days. If X is three times as efficient as Z, how many days does it take for Y to complete the task alone?

  1. 24

  2. 30

  3. 36

  4. 40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let X, Y, Z be their daily work rates. X+Y = 1/15, Y+Z = 1/20. Given X = 3Z. Substituting X: 3Z+Y = 1/15 and Y+Z = 1/20. Subtracting the equations: 2Z = 1/15 - 1/20 = 1/60, so Z = 1/120. Then Y = 1/20 - 1/120 = 5/120 = 1/24. Y takes 24 days.

Multiple choice

A team of 7 technicians is tasked with repairing a fleet of buses within 50 days, working 8 hours a day. After 10 days, one technician leaves the project. After another 20 days, two more technicians leave. The remaining technicians decide to work 10 hours a day to complete the project on time. By what percentage must the remaining technicians increase their work rate to finish within the specified time?

  1. 50%

  2. 60%

  3. 70%

  4. 80%

  5. 90%
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Riya and Siya together can complete a task in 200/3 days, while Siya and Tiya together can complete the same task in 120 days. Riya starts working on the task and works for 50 days, then Siya takes over and works for 40 days. Finally, Tiya takes over and completes the remaining task in 90 days. If Riya had started the task alone and worked on all days, Siya had worked on every second day, and Tiya had worked on every third day, then on which day would the task be completed?

  1. 30th

  2. 45th

  3. 74th

  4. 97th
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Mohan can do a piece of work in 25 days alone and Rohan can finish it in 20 days. They work together for 5 days & then Mohan left the work. In how many days will Rohan finish the remaining work?

  1. 20 days

  2. 9 days

  3. 14 days

  4. 11 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mohan's rate is 1/25, Rohan's is 1/20. Together they work at (1/25 + 1/20) = 9/100 per day. In 5 days, they complete 5 * 9/100 = 45/100 = 9/20 of the work. Remaining work is 11/20. Rohan finishes this in (11/20) / (1/20) = 11 days.