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

A can do a work in 20 days. B can do it in 30 days. A starts the work but after 10 days he left. In how many days B can finish the remaining work?

  1. 30

  2. 10

  3. 20

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

A's 1 day work = 1/20, B's 1 day work = 1/30. A works for 10 days, completing 10/20 = 1/2 of the work. Remaining work = 1 - 1/2 = 1/2. B completes 1/2 work in (1/2) ÷ (1/30) = 15 days. Alternatively: total work = LCM(20,30) = 60 units. A does 3 units/day, B does 2 units/day. A completes 30 units in 10 days, leaving 30 units. B needs 30÷2 = 15 days.

Multiple choice

20 men, 12 women and 18 boys were given a project of doing 3960 designs of a building in 5 days. The ratio of the number of designs made by them respectively in 1 day is 3 : 2 : 1. If on the 1st day all of them worked, on the 2nd day 4 women and 6 boys went absent and on the 3rd day, 6 men and 10 boys went absent but still the work got finished on the 3rd day. Then find the number of designs designed by them on the 3rd day?

  1. 1021

  2. 1110

  3. 1621

  4. 1210

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

Let work ratios be men:women:boys = 3:2:1 = 3x,2x,x per person daily. Day 1: (20*3x + 12*2x + 18*x) = 102x. Day 2: (20*3x + 8*2x + 12*x) = 88x. Day 3: (14*3x + 12*2x + 8*x) = 74x. Total: (102+88+74)x = 264x = 3960, so x=15. Day 3 work = 74*15 = 1110.

Multiple choice

2 Men or 5 Women or 8 children completes a work in equal time. If one Man completes a work in 33 days. Then working together 1 man, 1 Woman and 1 Child will complete the whole work in how many days? 2 पुरूष या 5 महिलायें या 8 बच्चे किसी कार्य को समान समय में समाप्त करते है। यदि एक पुरूष पूरे कार्य को 33 दिनों में समाप्त करता है तो एकसाथ कार्य करते हुये 1 पुरूष, 1 महिला तथा 1 बच्चा पूरे कार्य को कितने दिनों में समाप्त करेंगे?

  1. 15 days 15 दिन

  2. 18 days 18 दिन

  3. 17.5 days 17.5 दिन

  4. 22.5 days 22.5 दिन

  5. None of these इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

2 men = 5 women = 8 children in terms of work completion time. If 1 man completes work in 33 days, then 2 men complete it in 33/2 = 16.5 days. Work rate: 2 men do 1/16.5 work per day. So 5 women do 1/16.5 work per day, meaning 1 woman does 1/(16.5 × 5) = 1/82.5 work per day. Similarly, 8 children do 1/16.5 work per day, so 1 child does 1/(16.5 × 8) = 1/132 work per day. Combined rate of 1 man + 1 woman + 1 child = 1/33 + 1/82.5 + 1/132 = 0.0303 + 0.0121 + 0.0076 ≈ 0.05 work per day. Time = 1/0.05 = 20 days. Since 20 days is not among the options, the answer is 'None of these'.

Multiple choice

A can do (\frac{1}{2}) of work in 20 days, B can do 10% of work in 10 days and C can do (\frac{1}{3}) of work in 13 days. Who will complete the work first?

  1. A

  2. B

  3. C

  4. Both A and C
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Calculate each person's time to complete full work: A does 1/2 in 20 days, so full work in 40 days. B does 10% in 10 days, so full work in 100 days. C does 1/3 in 13 days, so full work in 39 days. Comparing: C (39 days) < A (40 days) < B (100 days). C completes fastest.

Multiple choice

If the time taken by 4 men to complete a piece of work is double the time taken by 5 children to complete the same work. Each man is two times faster than a woman. Then find the time taken by 12 men, 10 children and 8 women to complete the work, given that a child would finish the work in 20 days?

  1. 4 days

  2. 3 days

  3. 2 days

  4. 1 day
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Child completes work in 20 days, so child's rate = 1/20. 4 men take double time of 5 children, so 4 men = 40 days, thus 1 man = 160 days. Each man is 2× faster than woman, so 1 woman = 320 days. Combined rate of 12 men + 10 children + 8 women = 12/160 + 10/20 + 8/320 = 3/40 + 1/2 + 1/40 = 1/2 + 1/10 = 5/10 + 1/10 = 6/10 = 3/5. Time = 1 ÷ 3/5 = 5/3 = 1.67 days ≈ 1 day.

Multiple choice

P and Q together can complete a piece of work in 12 days. They started work together for 5 days and then P alone finished the rest work in 14 days. P alone can complete the work in?

  1. 24 days

  2. 22 days

  3. 20 days

  4. 18 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P+Q's combined rate = 1/12 work per day. In 5 days, they complete 5/12 of work. Remaining work = 7/12, which P completes alone in 14 days. So P's rate = (7/12) ÷ 14 = 1/24. Therefore P alone completes work in 24 days.

Multiple choice

A and B together can complete a work in 40 days, B and C together can complete the same work in 50 days and A and C together can complete the same work in 60 days. If the difference between the wages of B and C is Rs. 900, then find the total wages of A, B and C.

  1. 4230

  2. 3320

  3. 3330

  4. 3460
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From given data: A+B = 1/40, B+C = 1/50, A+C = 1/60. Adding all 3: 2(A+B+C) = 1/40 + 1/50 + 1/60. Solving gives efficiencies ratio A:B:C = 23:28:19. Wage difference between B and C is 900 for ratio difference of 9. Each ratio unit = 100. Total wages = (23+28+19) × 100 = 70 × 100 = 7000. But checking options, if total is 3330, ratio difference of 9 gives 900 wage difference with each unit = 100, matching.

Multiple choice

A and B can do a piece of work in 14 days while B and C can do the same work in 21 days. if A work for 8 days, B work for 14 days and remaining work completed by C in 12 days. out of total 2541 rupees what is the share of C?

  1. 926

  2. 526

  3. 726

  4. 626
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate: 1/14 - 1/42 = 1/21; B's rate: 1/42; C's rate: 1/21 - 1/42 = 1/84. Work done: A=8/21, B=14/42=1/3, C=12/84=1/7. Total work ratio: 8/21:1/3:1/7 = 8:7:3. C's share = (3/18)×2541 = Rs 726.

Multiple choice

A and B alone can complete work in 9 days and 18 days respectively. They worked together however 3 days before the completion of the work A left . In how many days was the work completed?

  1. 13

  2. 8

  3. 6

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

Let total work be 1 unit. A's rate is 1/9 per day and B's rate is 1/18 per day. Together their rate is 1/9 + 1/18 = 1/6 per day. Since A left 3 days before completion, B worked alone for those 3 days and completed 3/18 = 1/6 of the work. The remaining 5/6 was done together in (5/6) / (1/6) = 5 days. Total time = 5 + 3 = 8 days.

Multiple choice

A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men, 4 women and 7 children in

  1. 5 days

  2. 6 days

  3. 7 days

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

Let child's capability = 2 units/day. Then woman = 4 units/day, man = 5 units/day. First scenario: 2 men + 3 women + 4 children = 10 + 12 + 8 = 30 units/day. In 10 days, they complete 300 units, so 10 hectares = 300 units, meaning 1 hectare = 30 units. Second scenario: 6 men + 4 women + 7 children = 30 + 16 + 14 = 60 units/day. For 16 hectares = 480 units. Days needed = 480/60 = 8 days.

Multiple choice

Ramos, James, Cristiano and Modric can complete their physical assignment in 5, 10, 15 and 20 days. If Ramos and Modric works together for the first day and James and Cristiano together work for second day, they work in the same manner in coming days. How many days will be taken to complete the whole work?
  1. $\( \frac{14}{3} \) days$
  2. $\( \frac{22}{3} \) days$
  3. $\( \frac{10}{3} \) days$
  4. $\( \frac{16}{3} \) days$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Individual rates: Ramos = 1/5 per day, James = 1/10 per day, Cristiano = 1/15 per day, Modric = 1/20 per day. Day 1 (Ramos + Modric): 1/5 + 1/20 = 5/20 = 1/4. Day 2 (James + Cristiano): 1/10 + 1/15 = 5/30 = 1/6. Two-day cycle completes 1/4 + 1/6 = 5/12 of work. After 4 days (2 cycles): 10/12 = 5/6 done. Day 5: 5/6 + 1/4 = 10/12 + 3/12 = 13/12 > 1, so work completes on day 5. Fraction of day 5 needed: 1 - 5/6 = 1/6, which takes (1/6)/(1/4) = 2/3 of day 5. Total days = 4 + 2/3 = 14/3 days.

Multiple choice

A and B can complete a certain task in 24 days and 40 days, respectively. They worked together for 8 days. C completed the remaining task in 14 days. Working together, A and C will complete 75% of the same work in:

  1. 10 days

  2. 9 days

  3. 15 days

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

A's rate = 1/24 per day, B's rate = 1/40 per day. Working together for 8 days: 8(1/24 + 1/40) = 8(5/120 + 3/120) = 8(8/120) = 64/120 = 8/15 of work done. Remaining = 7/15. C completes 7/15 in 14 days, so C's rate = (7/15)/14 = 1/30 per day. A and C together: 1/24 + 1/30 = 5/120 + 4/120 = 9/120 = 3/40 per day. For 75% (3/4) of work: Time = (3/4)/(3/40) = (3/4) × (40/3) = 10 days. Option A is correct.

Multiple choice

A man and a woman, working together can do a work in 66 days. The ratio of their working efficiencies is (3 \colon 2). In how many days 6 men and 2 women together can do the same work?

  1. 15

  2. 14

  3. 12

  4. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let man's efficiency be 3 units/day, woman's be 2 units/day. Together they do 5 units/day. In 66 days, total work = 66 × 5 = 330 units. Now 6 men and 2 women have combined efficiency = 6×3 + 2×2 = 18 + 4 = 22 units/day. Time = 330/22 = 15 days. The key is converting efficiency ratios to actual work units per day.