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 and Y can do a piece of work in 45 days and 40 days, respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to?

  1. 8

  2. 9

  3. 10

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

X does 1/45 per day, Y does 1/40 per day. Together for n days: n(1/45 + 1/40) = n(8+9)/360 = 17n/360. Y works alone for 23 days: 23/40 = 207/360. 17n/360 + 207/360 = 1. 17n = 360 - 207 = 153. n = 153/17 = 9.

Multiple choice

480 persons working 10 hours per day complete one-fourth of a work in 10 days. How many additional persons are to be employed in order to complete the remaining work in 20 days, working 8 hours per day?

  1. 400

  2. 420

  3. 480

  4. 500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work done = 480 * 10 * 10 = 48000 man-hours for 1/4 work. Total work = 192000 man-hours. Remaining work = 144000 man-hours. Required men = 144000 / (20 * 8) = 144000 / 160 = 900. Additional men = 900 - 480 = 420.

Multiple choice

12 women and 16 men can do a piece of work in 5 days. 13 women and 24 men can do it in 4 days. How long will 25 women and 50 men take to do it?

  1. 1 day

  2. 2 days

  3. 3 days

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

Let W be work per woman and M be work per man. 5(12W + 16M) = 1, so 60W + 80M = 1. 4(13W + 24M) = 1, so 52W + 96M = 1. Solving the system: 60W + 80M = 52W + 96M => 8W = 16M => W = 2M. Substituting: 60(2M) + 80M = 1 => 200M = 1 => M = 1/200, W = 1/100. For 25W + 50M: 25(1/100) + 50(1/200) = 0.25 + 0.25 = 0.5. Time = 1/0.5 = 2 days.

Multiple choice

A and B together can complete some work in 36 days. B and C together can complete the same work in 60 days. A and C together can complete the same work in 45 days. In how many days can B alone complete the same work?

  1. 180 days

  2. 60 days

  3. 100 days

  4. 90 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given 1/A + 1/B = 1/36, 1/B + 1/C = 1/60, and 1/A + 1/C = 1/45. Adding these gives 2(1/A + 1/B + 1/C) = 1/36 + 1/60 + 1/45 = 12/180 = 1/15. Thus, 1/A + 1/B + 1/C = 1/30. Subtracting (1/A + 1/C) from this gives 1/B = 1/30 - 1/45 = 1/90, so B takes 90 days.

Multiple choice

Tina alone can do a piece of work in 12 days and Meena alone can do the same work in 15 days. If Tina and Meena undertook this work for Rs. 18,000, then how much amount will Meena get, if they work together?

  1. Rs. 10,000

  2. Rs. 6,000

  3. Rs. 12,000

  4. Rs. 8,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Tina's rate is 1/12 and Meena's rate is 1/15. The ratio of their work capacities is (1/12) : (1/15) = 5 : 4. Meena's share of the 18,000 is (4 / (5+4)) * 18,000 = (4/9) * 18,000 = 8,000.

Multiple choice

A can do a certain work at twice the speed of B. Further, B can do the same work at 1.5 times the speed of C. All of them together can finish the work in 12 days. In how many days can C alone finish the work?

  1. 36 days

  2. 45 days

  3. 60 days

  4. 66 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let rate of C = c. Rate of B = 1.5c. Rate of A = 2 * (1.5c) = 3c. Combined rate = 3c + 1.5c + c = 5.5c. Work = Rate * Time = 5.5c * 12 = 66c. Time for C = Work / c = 66c / c = 66 days.

Multiple choice

If 17 women and 24 men can do a piece of work in 5 days and 12 women and 23 men can do it in 6 days, then which one of the following is correct?

  1. Efficiency of 13 women = Efficiency of 18 men

  2. Efficiency of 11 women = Efficiency of 16 men

  3. Efficiency of 13 women = Efficiency of 17 men

  4. Efficiency of 11 women = Efficiency of 15 men
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let W be efficiency of a woman, M be efficiency of a man. (17W + 24M) * 5 = (12W + 23M) * 6. 85W + 120M = 72W + 138M. 13W = 18M.

Multiple choice

Tamal and Tina can independently complete a certain job in four days and nine days respectively. They together started the work, but after two days both left and the remaining work was completed by Trisha in two more days. How long, in days, will Trisha alone complete the entire job?

  1. 7.2

  2. 8

  3. 12

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Tamal's rate is 1/4 per day, Tina's is 1/9 per day. Combined rate is 1/4 + 1/9 = 13/36. In 2 days, they complete 2 * (13/36) = 13/18 of the work. Remaining work is 5/18. Trisha completes 5/18 in 2 days, so her rate is (5/18) / 2 = 5/36 per day. Time for Trisha to finish the whole job is 36/5 = 7.2 days.

Multiple choice

A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5 of the work is finished. How many additional men may be employed so that the work may be completed on time, if each man is working 9 hours per day now?

  1. 56

  2. 65

  3. 46

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work done = 104 * 30 * 8 = 24960 man-hours. This is 2/5 of total work, so total work = 62400 man-hours. Remaining work = 37440 man-hours. Time remaining = 56 - 30 = 26 days. Men needed = 37440 / (26 * 9) = 160. Additional men = 160 - 104 = 56.