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 complete some work in 35 days and B can complete the same work in 15 days. They worked together for 8 days, then B left the work. In how many days will A alone complete 60% of the remaining work?

  1. 5

  2. 10

  3. 8

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

A's rate is 1/35 per day, B's rate is 1/15 per day. Combined rate = 2/21 per day. Work done in 8 days = 16/21. Remaining work = 5/21. 60% of remaining = 3/21 = 1/7. Time for A to complete 1/7 = (1/7)/(1/35) = 5 days. The key is to first find the combined work rate, then calculate the remaining portion after 8 days.

Multiple choice

A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 60% of the job?

  1. 18 days

  2. 30 days

  3. 25 days

  4. 24 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/10 job/day, B's rate = 1/5 job/day. Together they do 3/10 per day. In 2 days: 6/10 = 3/5 done. Remaining: 2/5. A + C do 2/5 in 3 days, so A+C rate = 2/15 per day. C's rate = 2/15 - 1/10 = 1/30 job/day. C alone needs 30 days for full job, so 60% takes 18 days.

Multiple choice

A, B and C can do a work in 36, 72 and 54 days respectively. They started the work together but A left 8 days before the completion of the work and C left 12 days before the completion of the work. In how many days was the work completed? A, B तथा C किसी काम को क्रमशः 36, 72 और 54 दिन में कर सकते हैं। उन्होंने मिलकर काम करना प्रारंभ किया लेकिन A काम पूरा होने से 8 दिन पहले ही चला गया और C काम पूरा होने से 12 दिन पहले काम छोड़कर चला गया। वह काम कितने दिनों में पूरा हुआ?

  1. 21

  2. 20

  3. 24

  4. 25

  5. None of these / इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total work be LCM(36,72,54)=216 units. A's rate=6/day, B's rate=3/day, C's rate=4/day. If work completes in D days: A works D-8 days (6D-48 units), C works D-12 days (4D-48 units), B works D days (3D units). Total: 13D-96=216, so 13D=312, D=24 days.

Multiple choice

A can do a certain work in 30 days. B is 25% more efficient than A, and C is 20% more efficient than B. A and B work together for 10 days. C alone completes the remaining work in x days. The value of x is:
  1. $4$
  2. $6$
  3. $8$
  4. $5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total work = 30 units (LCM of 30). A's efficiency = 30/30 = 1 unit/day. B is 25% more efficient than A, so B's efficiency = 1.25 units/day. C is 20% more efficient than B, so C's efficiency = 1.25 × 1.2 = 1.5 units/day. Work done by A and B in 10 days = (1 + 1.25) × 10 = 22.5 units. Remaining work = 30 - 22.5 = 7.5 units. Time for C alone = 7.5/1.5 = 5 days. This matches option D.

Multiple choice

A can do 33.33% of a work in 10 days, and B can do 20% of the same work in 9 days. They worked together for 8 days. C alone completed 30% of the remaining work in 10 days. A and C together can do the same work in

  1. 18

  2. 12

  3. 15

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

A does 33.33% (1/3) of work in 10 days, so total work in 30 days. A's rate = 1/30 work/day. B does 20% (1/5) of work in 9 days, so total work in 45 days. B's rate = 1/45 work/day. Work done by A and B together in 8 days = 8(1/30 + 1/45) = 8(3/90 + 2/90) = 8(5/90) = 40/90 = 4/9 of work. Remaining = 5/9. C does 30% of remaining (5/9) in 10 days, so C does 0.3 × 5/9 = 1/6 of total work in 10 days. C's rate = 1/60 work/day. A and C together: 1/30 + 1/60 = 3/60 = 1/20 work/day, so they complete the work in 20 days.

Multiple choice

A and B can complete a task in 70 days, B and C can complete it in 52.5 days while C and A can do the same task together in 42 days. How many days will each of A, B, and C take to complete the task individually?

  1. 105, 210 and 70

  2. 56, 84 and 168

  3. 70, 10 and 105

  4. 84, 168 and 56
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C's individual days be a, b, c. Combined rates: A+B = 1/70, B+C = 1/52.5 = 2/105, C+A = 1/42. Adding all three: 2(A+B+C) = 1/70 + 2/105 + 1/42. LCD of 70, 105, 42 is 210. So: 2(A+B+C) = 3/210 + 4/210 + 5/210 = 12/210 = 2/35. Thus A+B+C = 1/35. To find individual rates: (A+B+C) - (B+C) = A = 1/35 - 2/105 = 3/105 - 2/105 = 1/105, so A = 105 days. Similarly, B = 1/35 - 1/42 = 6/210 - 5/210 = 1/210, so B = 210 days. And C = 1/35 - 1/70 = 2/70 - 1/70 = 1/70, so C = 70 days. The answer (105, 210, 70) matches option A. However, the topic is incorrectly listed as 'Clocks & Calendars/Leap Year' when it should be 'Time and Work'.

Multiple choice

In how many days will 5 men and 4 women together complete the work?()(I). 15 men and 12 women can complete the same work in 12 days.()(II). 10 men and 8 women can complete the same work in 16 days.

  1. Only II

  2. Only I

  3. From I and II

  4. Either from I or II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Both statements give equivalent information about the relationship between men and women's work rates. From I: (15 men + 12 women) = 12 days. From II: (10 men + 8 women) = 16 days. Both simplify to the same ratio, so either is sufficient.

Multiple choice

16 men or 20 women completes a work in 24 days. 8 men and 30 women will complete the same work in how many days? 16 पुरुष या 20 महिलाएं एक कार्य 24 दिनों में पूरा करते हैं । 8 पुरुष और 30 महिलाएं एक साथ कार्य करते हुए कार्य को कितने दिनों में पूरा करेंगे?

  1. 15 days 15 दिन

  2. 18 days 18 दिन

  3. 24 days 24 दिन

  4. 20 days 20 दिन

  5. 12 days 12 दिन
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

16 men complete work in 24 days, so 16 men's 1 day work = 1/24. 1 man's 1 day work = 1/(16×24) = 1/384. Similarly, 20 women complete in 24 days, so 1 woman's 1 day work = 1/(20×24) = 1/480. 8 men + 30 women's combined 1 day work = 8/384 + 30/480 = 1/48 + 1/16 = 1/48 + 3/48 = 4/48 = 1/12. Therefore they complete the work in 12 days, which is option E.

Multiple choice

Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?

  1. 38 days

  2. 54 days

  3. 44 days

  4. 56 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m be the work done by one man in one day, and w be the work done by one woman in one day. From the first condition: 4m + 3w = 1/6 (since they complete 1 job in 6 days). From the second: 5m + 6w = 1/4. Solving these equations: Multiply first by 5: 20m + 15w = 5/6. Multiply second by 4: 20m + 24w = 1. Subtracting: 9w = 1/6, so w = 1/54. Therefore, one woman alone takes 54 days.

Multiple choice

A can finish a piece of the work in 16 days and B can finish it in 12 days. They worked together for 4 days and then A left. B finished the remaining work. For how many total number of days did B work to finish the work completely?

  1. 6

  2. 9

  3. 4

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

A's 1 day work = 1/16, B's 1 day work = 1/12. Working together for 4 days, they complete 4(1/16 + 1/12) = 4(7/48) = 7/12 of the work. Remaining work = 5/12. B alone does this in (5/12)/(1/12) = 5 days. B worked for 4 days with A + 5 days alone = 9 days total.

Multiple choice

A, B and C together can build a wall in 18 days. C is three times as productive as B and A alone can build the wall in 54 days. In how many days A and B working together can build the wall?

  1. 53 days

  2. 46 days

  3. 42 days

  4. 36 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total work = 1 unit. A+B+C combined rate = 1/18. A's rate = 1/54. So B+C = 1/18-1/54 = 3/54-1/54 = 2/54 = 1/27. Given C is 3 times as productive as B, so C = 3B. Then B+3B = 4B = 1/27, so B = 1/108. A+B together = 1/54+1/108 = 2/108+1/108 = 3/108 = 1/36. Therefore, A and B together can build the wall in 36 days.

Multiple choice

Ram can do a work in 15 days. Ram and Shyam can do the same work in 10 days. If they got Rs 6000 for the work, find the share of Shyam?

  1. 2400 Rs

  2. 2000 Rs

  3. 1500 Rs

  4. 1600 Rs

  5. 1200 Rs
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ram's 1 day work = 1/15. Ram + Shyam's 1 day work = 1/10. So Shyam's 1 day work = 1/10 - 1/15 = (3-2)/30 = 1/30. This means Shyam alone takes 30 days. Their work ratio is (1/15):(1/30) = 2:1. So Shyam gets (1/3)×6000 = Rs 2000. Option B is correct.

Multiple choice

A can do a piece of work in 24 days. B can do the same work in 30 days and C in 40 days. A and C worked for 4 days and handed it to B. B worked for some days and handed it again to A and C 6 days before completing the work. For how many days did B work?

  1. 10 days

  2. 15 days

  3. 12 days

  4. 8 days

  5. 9 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work = 120 (LCM of 24,30,40). A's rate = 5/day, B's rate = 4/day, C's rate = 3/day. A+C work for 4 days: 8×4=32 work. Remaining work = 120-32=88. A+C work for last 6 days: 8×6=48 work. So B must have done 88-48=40 work. At 4/day, B worked for 40/4=10 days.

Multiple choice

A can do a piece of work in 10 days, B can do the same work in 12 days and C in 15 days. They all started working together, but A leaves the work after 2 days and B leaves the work 3 days before the work is completed. For how many days the work lasted? A एक काम को 10 दिनों में कर सकता है, B उसी काम को 12 दिनों में और C उसी काम को 15 दिनों में कर सकता है। वे सभी एक साथ काम करना शुरू करते हैं, लेकिन A 2 दिनों के बाद काम छोड़ देता है और B काम पूरा होने से 3 दिन पहले काम छोड़ देता है। कार्य कितने दिनों तक चला?

  1. 7 days 7 दिन

  2. 8 days 8 दिन

  3. 12 days 12 दिन

  4. 9 days 9 दिन

  5. 10 days 10 दिन
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work = LCM(10,12,15) = 60 units. Rates: A = 6, B = 5, C = 4 per day. If total days = d, A works 2 days (12 units), B works (d-3) days, C works d days. Equation: 12 + 5(d-3) + 4d = 60. Simplifying: 12 + 5d-15 + 4d = 60, so 9d = 63, d = 7 days.