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

Avinash, Biren and Chandu can complete a piece of work. Avinash and Biren together can finish the work in 16 days, while Biren and Chandu together can finish the same work in 24 days. Initially, Avinash and Biren start the work together. Avinash works for 4 days and then leaves. Biren continues and works for a total of 6 days from the start and then leaves. After that, Chandu completes the remaining work alone in the next 34 days. In how many days can Avinash and Chandu together complete the entire work?

  1. 8

  2. 10

  3. 12

  4. 16

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

Let rates be A, B, C. A+B = 1/16, B+C = 1/24. Avinash works 4 days, Biren 6 days, Chandu 34 days. 4A + 6B + 34C = 1. Since A+B=1/16, 4(A+B) + 2B + 34C = 1 => 4/16 + 2B + 34C = 1 => 2B + 34C = 3/4. Since B+C=1/24, 2(B+C) + 32C = 3/4 => 2/24 + 32C = 3/4 => 32C = 3/4 - 1/12 = 8/12 = 2/3. C = 2/96 = 1/48. B = 1/24 - 1/48 = 1/48. A = 1/16 - 1/48 = 2/48 = 1/24. A+C = 1/24 + 1/48 = 3/48 = 1/16. Time = 16 days.

Multiple choice

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of Rs. 21,000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

  1. 9000

  2. 9200

  3. 9100

  4. 9150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Anil's rate is 1/60, Bimal's is 1/84. In 10 days, Anil does 10/60 = 1/6. Remaining work is 5/6. In 14 days, Anil, Bimal, and Charu do 5/6. Rate of (A+B+C) = (5/6) / 14 = 5/84. Charu's rate = 5/84 - (1/60 + 1/84) = 5/84 - 12/420 = 25/420 - 12/420 = 13/420. Charu's share = (13/420) * 14 days * 21000 = 9100.

Multiple choice

One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

  1. 11.5

  2. 10

  3. 12.5

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let R and G be rates. R works 8 hours (9AM to 5PM), G works 6 hours. R*8 + G*6 = 1. If both work 7.5 hours (30 mins earlier), (R+G)*7.5 = 1. Solving the system: 8R + 6G = 7.5R + 7.5G -> 0.5R = 1.5G -> R = 3G. Substitute: (3G)*8 + 6G = 1 -> 30G = 1 -> G = 1/30. R = 3/30 = 1/10. Rahul takes 10 hours.

Multiple choice

A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

  1. 23

  2. 140

  3. 36

  4. 150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work = N * 7 * 10 = 70N. This is 35% of the project. So 100% = 70N / 0.35 = 200N. Remaining work is 65% = 130N. Remaining people = N - 10. Time = 14 days, 10 hours/day = 140 hours. (N-10) * 140 = 130N. 140N - 1400 = 130N. 10N = 1400, N = 140.

Multiple choice

Raj, Seema, and Tara have individual completion times of 25 days, 18 days, and 30 days for a particular task. While Raj is committed to working every day, Seema works on weekdays from Monday to Friday, and Tara works on weekends i.e. Saturday and Sunday. With this schedule starting from Monday what will be the approximate time required for them to finish the task together?

  1. 11 days

  2. 13 days

  3. 9 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Weekly work: Raj does 7/25, Seema does 5/18, Tara does 2/30. Weekly total = 7/25 + 5/18 + 2/30 = 126/450 + 125/450 + 30/450 = 281/450. Time = 450/281 approx 1.6 weeks = 11.2 days.

Multiple choice

Two workers, A and B, are hired to complete a construction project. Worker A can complete the project in 20 days, while worker B can complete the project in 25 days. A and B start the work, however after working together for 5 days, worker A leaves due to unforeseen circumstances. To complete the remaining work, worker B hires worker C, who can alone complete the project in 30 days. How many more days will it take for B and C to complete the remaining project?

  1. 5.5 days

  2. 8.5 days

  3. 7.5 days

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

A's rate = 1/20, B's rate = 1/25. Together rate = 1/20 + 1/25 = 9/100. In 5 days, they do 5 * 9/100 = 45/100 = 9/20. Remaining work = 11/20. B and C rate = 1/25 + 1/30 = 11/150. Time = (11/20) / (11/150) = 150/20 = 7.5 days.

Multiple choice

A can do a piece of work in 40 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?

  1. 17 1/2 days

  2. 44 days

  3. 24 days

  4. 30 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work in 10 days = 10/40 = 1/4. B's work in 10 days = 10/30 = 1/3. Remaining work = 1 - (1/4 + 1/3) = 1 - 7/12 = 5/12. C does 5/12 of the work in 10 days, so C does the whole work in 10 * (12/5) = 24 days.

Multiple choice

A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.

  1. 2 days

  2. 1 ½ days

  3. 3 days

  4. 3 ½ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's rate is 3/20 work/day and B's rate is 1/5 work/day. Together, they do (3/20 + 4/20) = 7/20 work/day. In 2 days, they complete 14/20 = 7/10 of the work. The remaining 3/10 work is done by B at 1/5 per day, taking (3/10) / (1/5) = 1.5 days.