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 piece of work in 4 days, B in 12 days and C in 6 days. If A is assisted by both B and C on every third day, the total work can be done in-

  1. 6 days

  2. 3 days

  3. 5 days

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

Work rates: A = 1/4, B = 1/12, C = 1/6 per day. Pattern: A works alone days 1-2, A+B+C work day 3. Each 3-day cycle: 2(1/4) + (1/4 + 1/12 + 1/6) = 5/6. After 2 cycles (6 days): 5/6 done. Day 7: A alone completes remaining 1/6. Option A (6 days) misses the final day.

Multiple choice

20 men could complete a work in 80 days. They worked together for 60 days, after that due to bad weather the work is stopped for 10 days. How many more men should be employed so as to complete the work in time?

  1. 12

  2. 10

  3. 15

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In 60 days, 20 men complete 60/80 = 3/4 of the work. Remaining 1/4 work must be done in 10 days by adding m men. Work rate equation: (20+m) × 10 = (1/4) × 20 × 80 = 400 man-days. Solving: 200 + 10m = 400, giving m = 20. So 20 additional men are needed to complete the remaining work in the stipulated time.

Multiple choice

M and N can do a piece of work in 25 days and 30 days respectively. They work together for 5 days and then M leaves the work. N will finish the rest of the work in how many days?

  1. 18 days

  2. 19 days

  3. 20 days

  4. 21 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

M's rate = 1/25, N's rate = 1/30. Combined rate = 1/25 + 1/30 = 11/150. In 5 days, they complete 5*(11/150) = 11/30 of work. Remaining = 19/30. N alone needs (19/30)/(1/30) = 19 days. The key is finding individual work rates and tracking remaining work.

Multiple choice

If A ,B and C can do a job working alone in 12, 18 an 36 days respectively. They all together work for 2 days, then B quits. How many days will A and C take to finish the rest of the amount ?

  1. 6 days

  2. 5 days

  3. 8 days

  4. 9 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Combined rate of A, B, C = (1/12 + 1/18 + 1/36) = (3+2+1)/36 = 6/36 = 1/6. In 2 days, they complete 2×(1/6) = 1/3 of work. Remaining work = 1 - 1/3 = 2/3. After B quits, A + C rate = (1/12 + 1/36) = (3+1)/36 = 4/36 = 1/9. Time needed = (2/3) ÷ (1/9) = (2/3)×9 = 6 days.

Multiple choice

A,B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days B leaves the job in how many days the total work will be completed?

  1. 10

  2. 12

  3. 15

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

LCM of 20, 24, 30 is 120 units. A's rate=6 units/day, B's rate=5 units/day, C's rate=4 units/day. First 4 days: all work together at 15 units/day → 60 units done. Remaining 60 units done by A+C at 10 units/day → 6 more days. The question asks total time, which is 4+6=10 days. Option A is correct.

Multiple choice

The ratio of efficiency of A,B,C is 4:5:3. Working together, they can complete that work in 25 days. A and C together will complete 35% of that work in how many days?

  1. 12

  2. 10

  3. 18

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

Let efficiencies be 4k, 5k, 3k for A,B,C. Combined efficiency = 12k units/day. In 25 days, total work = 25×12k = 300k units. A and C together have efficiency 7k units/day. To complete 35% of work = 0.35×300k = 105k units, they need 105k/(7k) = 15 days.

Multiple choice

C is 5 times as efficient as B. A takes 60 days to complete a task. If A, B and C working together can complete the task in 12 days. In how many days can B complete the task if he worked alone?

  1. 80

  2. 75

  3. 90

  4. 95
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

C is 5 times as efficient as B, so C's work rate is 5 times B's rate. If B alone takes x days, B's rate is 1/x and C's rate is 5/x. A takes 60 days (rate 1/60). Together: 1/60 + 1/x + 5/x = 1/12. Solving: 1/60 + 6/x = 1/12, so 6/x = 1/12 - 1/60 = 4/60 = 1/15, giving x = 90.

Multiple choice

4 Men can complete a piece of work in 58 days. They started the work together but at the end of every 5th day one man leaves the work and in the place of the man, one woman joins the work and the women continue doing the work and finish it despite all the men left in the mid of the work. Find the total number of days they take to complete the work in this manner if the efficiency of one women is 25% of the efficiency of one man.
  1. $174.5 days$
  2. $194.5 days$
  3. $116 days$
  4. $174 days$

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

4 men complete work in 58 days, so total work = 4 × 58 = 232 man-days. Women have 25% efficiency, so 1 woman = 0.25 man. Every 5 days, 1 man is replaced by 1 woman. Days 1-5: 4M → 20 work. Days 6-10: 3M+1W → 5×3.25 = 16.25. Days 11-15: 2M+2W → 5×2.5 = 12.5. Days 16-20: 1M+3W → 5×1.75 = 8.75. Days 21+: 4W → 5×1 = 5 per cycle. After 20 days: 57.5 work done. Remaining: 174.5. At 5 per 5-day cycle: 34.95 × 5 = 174.75. Total: 20 + 174.75 = 194.75 ≈ 194.5.

Multiple choice

Aman is thrice as efficient as Vikash. Aman started the work and worked for 6 days then he is replaced by Vikash. He worked for 9 more days and they together finish 50% of the work. Find in how many days Vikash can complete the work?

  1. 35 days

  2. 40 days

  3. 45 days

  4. 50 days

  5. 54 days
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

माना विकाश की दक्षता 1, तो अमन की दक्षता 3। विकाश को 1 काम पूरा करने में 54 दिन लगेंगे। अमन 6 दिन काम करता है = 18 इकाई काम। विकाश 9 दिन काम करता है = 9 इकाई काम। कुल 27 इकाई = 50% काम, तो पूरा काम = 54 इकाई। विकाश अकेला 54 दिन में पूरा करेगा। विकल्प E सही है।

Multiple choice

If 12 men and 16 boys can do a piece of work in 20 days while 52 men and 96 boys can do the same work in 4 days, the time taken by 15 men and 20 boys in doing the same type of work will be?

  1. 12

  2. 14

  3. 15

  4. 16

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

Set up equations: Let m and b be work done by one man and one boy per day. From (12m + 16b) × 20 = (52m + 96b) × 4, we get m = 2b. Total work = 800b. For 15 men + 20 boys = 50b, days = 800b ÷ 50b = 16 days. The key is finding the relationship between men's and boys' work capacity.

Multiple choice

A and B can complete the some work in 12 and 15 days respectively. They started working together but 3 days before the completion of the work B leaves the work. Find in how many days the work will be completed?

  1. 8

  2. 7

  3. 6

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

Let total work be 60 units. A's rate = 5 units/day, B's rate = 4 units/day. B leaves 3 days before completion, so A works alone for 3 days, completing 15 units. Remaining 45 units done together at 9 units/day = 5 days. Total = 5 + 3 = 8 days.

Multiple choice

A can completes a work in 15 days and B in 25 days. A and B together work for 5 days. Then A goes for a leave of 5 days. When A returns then B leaves the work. For how many days A has to work alone to complete the whole work

  1. 5 days

  2. 6 days

  3. 2 days

  4. 8 days

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

Calculate A's rate = 1/15 per day and B's rate = 1/25 per day. Together they do 8/75 per day. In first 5 days (A+B): 5 × 8/75 = 8/15 work done. Next 5 days (B alone): 5 × 1/25 = 1/5 = 3/15 work done. Total done = 11/15, remaining = 4/15. A alone needs: (4/15) ÷ (1/15) = 4 days. Since 4 is not among options A-D, option E (None of these) is correct.

Multiple choice

A has done 1/3rd of work in 30 days, B complete the rest of job in 90 days. In how many days can they together do the job?

  1. 34 days

  2. 32 days

  3. 54 days

  4. 52 days

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

A completes 1/3 of work in 30 days, so A's full work time = 30 × 3 = 90 days, rate = 1/90 per day. B completes remaining 2/3 work in 90 days, so B's full work time = 90 × 3/2 = 135 days, rate = 1/135 per day. Combined rate = 1/90 + 1/135 = 3/270 + 2/270 = 5/270 = 1/54. Together they complete the work in 54 days.

Multiple choice

A is 50% more efficient than B and C is 40 % less efficient than B. Working together they can complete a task in 10 days . in how many days will A alone complete 150% of the work?

  1. 32

  2. 35

  3. 31

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

Let B's efficiency be 100 units/day. Then A's efficiency is 150 (50% more) and C's efficiency is 60 (40% less). Combined efficiency = 150+100+60=310 units/day. Total work = 310×10=3100 units. A alone does 150% of 3100 = 4650 units. At 150 units/day, A needs 4650/150=31 days. If A took 35 days, efficiency would need to be about 133 units/day, not 150.

Multiple choice

A and B can complete a task in 36 days. However, A had to leave a few days before the task was completed and hence it took 54 days in all to complete the task. If A alone could complete the work in 48 days, how many days before the work getting over, did A leave?

  1. 25

  2. 30

  3. 24

  4. 28
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's work rate is 1/48 per day. Combined rate is 1/36 per day, so B's rate is 1/36 - 1/48 = 1/144 per day. Let A leave x days before completion. Then (A+B) work together for (54-x) days at rate 1/36, and B works alone for x days at rate 1/144. Setting (54-x)/36 + x/144 = 1 gives 216 - 3x = 144, so x = 24 days.