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

X can do a job in 10 days, Y in 15 days and Z in 18 days. Y and Z begin the work but have to leave after 3 days. How many days will X take to finish the job?

  1. 19/3 days

  2. 57/11 days

  3. 53/12 days

  4. 6.5 days

  5. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X, Y, and Z have rates of 1/10, 1/15, and 1/18 of the job per day. Y and Z work for 3 days, completing 3 * (1/15 + 1/18) = 3 * (6/90 + 5/90) = 3 * (11/90) = 11/30 of the job. X must finish the remaining 19/30 of the job at a rate of 1/10 per day, taking (19/30) / (1/10) = 19/3 days.

Multiple choice

A is 40% more efficient than B. How much time will they both take to complete the same piece of work which A alone can complete in 20 days ?

  1. 7 days

  2. 10(⅓) days

  3. 11(⅔) days

  4. 10 days

  5. None
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since A is 40% more efficient than B, their efficiency ratio is 140:100, or 7:5. If A completes the work in 20 days, the total work can be represented as 7 * 20 = 140 units. Working together, their combined efficiency is 7 + 5 = 12 units per day, so they will complete the work in 140 / 12 = 11 2/3 days.

Multiple choice

A can complete a work in 12 days and B can complete the same work in 18 days. A and B start the work together, but after 4 days, A leaves the work. C then joins B and together they finish the remaining work in 5 days. If the total wages paid for the work is ₹7200 and wages are divided in proportion to the work done, what is C's share of the wages?

  1. ₹1675

  2. ₹1079

  3. ₹1200

  4. ₹1145

  5. ₹1935
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/12, B's rate = 1/18. A and B work for 4 days: 4 * (1/12 + 1/18) = 4 * (5/36) = 5/9. Remaining work = 4/9. B and C do this in 5 days: 5 * (1/18 + C_rate) = 4/9. 1/18 + C_rate = 4/45. C_rate = 4/45 - 1/18 = (8-5)/90 = 3/90 = 1/30. Total work done by C = 5 * (1/30) = 5/30 = 1/6. C's share = (1/6) * 7200 = 1200.

Multiple choice

C completes work in 15 days. How many days A, B, C together? I: A & B together 5.625 days. II: B & C together 9 days.

  1. I alone sufficient

  2. II alone sufficient

  3. Either I or II sufficient

  4. Both not sufficient

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

We know C's rate is 1/15. Statement I gives A+B's rate as 1/5.625 = 16/90 = 8/45. Together A+B+C = 8/45 + 3/45 = 11/45. This is sufficient. Statement II gives B+C's rate as 1/9. We don't know A's rate. Thus, I alone is sufficient.

Multiple choice

A can complete a piece of work in 12 days, while B can complete the same work in 18 days. They start working together, but A leaves the work 3 days before its completion. In how many total days is the work finished?

  1. 8 days

  2. 9 days

  3. 7.5 days

  4. 6 days

  5. 8.4 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work be 36 units. A does 3 units/day, B does 2 units/day. Let total days be x. B works for x days, A works for x-3 days. 3(x-3) + 2x = 36. 3x - 9 + 2x = 36. 5x = 45. x = 9 days.

Multiple choice

Working efficiently, 16 industrial machines can produce a target output of 2400 structural units in 18 days working 8 hours a day. How many days will it take 24 identical machines to manufacture 3600 units if they run at an operational schedule of 9 hours a day?

  1. 16 days

  2. 18 days

  3. 20 days

  4. 22 days

  5. 15 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use the formula (M1 * D1 * H1) / W1 = (M2 * D2 * H2) / W2. (16 * 18 * 8) / 2400 = (24 * D2 * 9) / 3600. 2304 / 2400 = 216 * D2 / 3600. 0.96 = 0.06 * D2. D2 = 0.96 / 0.06 = 16 days.

Multiple choice

A man can complete a specific work in 20 days. Working together with a boy, they can complete the same work in 12 days. If the total earnings for the work is Rs 500 and the money is divided in proportion to the work done by each, what is the financial share of the boy?

  1. 150rs

  2. 180rs

  3. 200rs

  4. 220rs

  5. 240rs
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Man's rate = 1/20. Together rate = 1/12. Boy's rate = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. Ratio of work = 1/20 : 1/30 = 3:2. Boy's share = (2/5)*500 = 200.

Multiple choice

A contractor agrees to complete a work in 24 days. He employs 18 workers initially. After 8 days, he realizes that only 25% of the work has been completed. How many additional workers are required to complete the remaining work on time, assuming all workers work at the same rate?

  1. 18

  2. 24

  3. 9

  4. 12

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

Work done = 25% in 8 days with 18 workers. Remaining work = 75% in 16 days (24-8). Let X be total workers needed. (18 * 8) / 0.25 = (X * 16) / 0.75. 144 / 0.25 = 16X / 0.75. 576 = 21.33X. Or simply: 18 workers do 25% in 8 days. To do 75% in 16 days, we need (18 * 3) / 2 = 27 workers. Additional workers = 27 - 18 = 9.

Multiple choice

Directions: The problem contains a question followed by three statements A, B and C. Read the statements carefully and determine which of the given statements is/are sufficient to answer the question. What is the time taken by Rohit to complete the work, if Rohan can complete the same work in 40 days? A. Rohit is 50% more efficient than Rohan. B. Pankaj and Rohit working together can complete the same work in 10 days. C. Rohit is 50% less efficient than Pankaj.

  1. Only A is sufficient.

  2. Only B and C together are sufficient.

  3. Only C is sufficient.

  4. Either A alone or B and C together are sufficient.

  5. None of A, B and C is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A provides the efficiency ratio between Rohit and Rohan, allowing us to find Rohit's time. Statements B and C together allow us to find Pankaj's efficiency relative to Rohan and then Rohit's time. Thus, either A alone or B and C together are sufficient.