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 contractor hires Amitabh to complete the work, and Amitabh can do the work in 25 days. Amitabh worked for 5 days, and after that, Bindu completed it in 20 days. In how many days will Amitabh and Bindu together finish the work?
  1. $25/2 days$
  2. $25/8 days$
  3. $25/3 days$
  4. $25/4 days$

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

Amitabh completes 1/5 of work in 5 days, so his rate is 1/25 per day. Remaining 4/5 work is done by Bindu in 20 days, so her rate is (4/5)/20 = 1/25 per day. Together, their combined rate is 1/25 + 1/25 = 2/25 per day. Time to complete full work together: 1/(2/25) = 25/2 days.

Multiple choice

A, B and C can do a piece of work in 10 days, 12 days and 15 days respectively. They work together after 2 day A left the work and after 2 day B also left. Find in how many days the total work will complete?

  1. 5 days

  2. 7 days

  3. 8 days

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

Work rates: A=1/10, B=1/12, C=1/15 per day. Days 1-2: All work together. Rate = 1/10+1/12+1/15 = 6/60+5/60+4/60 = 15/60 = 1/4. Work done = 2×(1/4) = 1/2. Days 3-4: B and C work. Rate = 1/12+1/15 = 5/60+4/60 = 9/60 = 3/20. Work done = 2×(3/20) = 3/10. Total done = 1/2+3/10 = 8/10 = 4/5. Remaining = 1/5, C does it alone in (1/5)/(1/15) = 3 days. Total = 4+3 = 7 days.

Multiple choice

A can do a work in 8 days, B can do in 6 days and C can do in 8 days. First A and B started the work. After 3 days they gave up the work and C was engaged to complete the remaining work. How many days C takes to complete the remaining work? A एक काम को 8 दिनों में कर सकता है B, 6 दिनों में कर सकता है और C, 8 दिनों में कर सकता है। पहले A और B काम शुरू करते है। 3 दिनों बाद वे काम छोड़ देते हैं और C ने अकेले शेष काम को पूरा किया तो शेष काम पूरा करने में C को कितना समय लगा?

  1. 8 days/दिन

  2. 7 days/दिन

  3. 1 days/दिन

  4. 3 days/दिन
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/8 per day, B's rate = 1/6 per day. Combined work for 3 days = 3 × (1/8 + 1/6) = 3 × 7/24 = 7/8. Remaining work = 1 - 7/8 = 1/8. C's rate = 1/8 per day. Time for C = (1/8) / (1/8) = 1 day. Option C is correct. Options A (8 days), B (7 days), and D (3 days) don't match this calculation.

Multiple choice

Humpty can do a piece of work in 10 days and Dumpty alone can do it in 5 days. Humpty and Dumpty undertook to do it for Rs.400. With the help of their neighbor Johnny, they finished it in 2 days. Find the share of Johnny?
  1. $Rs. 120$
  2. $Rs. 200$
  3. $Rs. 180$
  4. $Rs. 160$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Humpty's rate = 1/10, Dumpty's rate = 1/5. Together they finish in 2 days, so combined rate with Johnny = 1/2. Johnny's rate = 1/2 - (1/10 + 1/5) = 1/2 - 3/10 = 2/10 = 1/5. Johnny contributes (1/5) × 2 = 2/5 of work. Share = (2/5) × 400 = Rs. 160. Option D is correct.

Multiple choice

25 days of Mike's wages can be paid by a certain sum of money. The same amount of money is sufficient to pay Chester's wages for 20 days. Find the number of days for which the money will be sufficient to pay the wages of both if they work together?

  1. 10 days

  2. 11 days
  3. $\(\frac{100}{9}\) days$
  4. $\(\frac{110}{9}\) days$

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

Mike works 25 days on the money, Chester works 20 days on the same money. Total money = M. Mike's daily wage = M/25, Chester's daily wage = M/20. Working together, their combined daily wage = M/25 + M/20 = 9M/100. Days the money lasts = M / (9M/100) = 100/9 = 11 1/9 days. Option C (100/9 days) matches.

Multiple choice

6 men or 17 women can paint a wall in 33 days. The number of days required to paint three such walls by 12 men and 32 women working at the same rate?

  1. 21.5

  2. 25.5

  3. 27

  4. 25

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

6 men paint 1 wall in 33 days, so 1 wall = 6 × 33 = 198 man-days. 17 women paint 1 wall in 33 days, so 1 wall = 17 × 33 = 561 woman-days. For 3 walls: total work = 3 × 198 = 594 man-days or 3 × 561 = 1683 woman-days. With 12 men and 32 women working together: daily work = 12/198 + 32/561 = 0.0606 + 0.0570 = 0.1176 walls. Days for 3 walls = 3/0.1176 ≈ 25.5 days. Option B matches.

Multiple choice

Vikas can do a piece of work in 12 days. Ramesh can do the same work in 15 days and Vimal in 20 days. Vikas and Vimal worked for 3 days and handed it to Ramesh. Ramesh worked for some days and handed it again to Vikas and Vimal 2 days before completing the work. For how many days did Ramesh work?

  1. 5 days

  2. 6 days

  3. 4 days

  4. 3 days

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

Vikas: 1/12 per day, Vimal: 1/20 per day, Ramesh: 1/15 per day. Vikas and Vimal work 3 days: 3(1/12 + 1/20) = 3(8/60) = 24/60 = 2/5 done. Ramesh works d days, then V + V work 2 days. d/15 + 2(1/12 + 1/20) = 3/5. d/15 + 16/60 = 36/60. d/15 = 20/60 = 1/3. d = 5 days.

Multiple choice

A and B can do a piece of work in 10 days and 15 days respectively. They begin to work together but B leaves after 2 days. In what time will A be able to complete the remaining work?
  1. $6\frac{1}{3} days$
  2. $7 days$
  3. $6\frac{2}{3} days$
  4. $8 days$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/10, B's rate = 1/15. Combined work in 2 days = 2(1/10+1/15) = 2(1/6) = 1/3. Remaining work = 2/3. A's time for 2/3 = (2/3) / (1/10) = 20/3 = 6 2/3 days. Option C is correct.

Multiple choice

If (\frac{4}{5}) part of a work is done by 12 men in 15 days, how many men will be required to complete the whole work in 25 days?

  1. 10 men

  2. 12 men

  3. 9 men

  4. 11 men
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 4/5 of work requires 12 men × 15 days = 180 man-days, then complete work needs 180 × 5/4 = 225 man-days. To finish in 25 days: 225/25 = 9 men. Option A (10 men) would be correct if you incorrectly used direct proportion without accounting for the 4/5 fraction properly.

Multiple choice

A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B takes (18 + d) days to complete the same work. A works for 4 days. The remaining work will be completed by B alone, in:

  1. 24 days

  2. 16 days

  3. 18 days

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

Combined rate: 1/(8+d) + 1/(18+d) = 1/d. Solving gives d = 12. A's rate = 1/20 per day. In 4 days, A completes 4/20 = 1/5 of work. Remaining work = 4/5. B's rate = 1/30 per day. Time for B = (4/5)/(1/30) = 24 days.

Multiple choice

A and B can complete a piece of work in 8 days, B and C can do it in 12 days, C and A can do it in 6 days. If B works for all the days. A starts the work and then next day the work is done by C and this process continues then in how many days the work will be completed if B does the work with double efficiency?

  1. 8 days

  2. 16 days

  3. 20 days

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

Find individual rates: A+B's rate = 1/8, B+C = 1/12, C+A = 1/6. Adding all: 2(A+B+C) = 1/8+1/12+1/6 = 9/24, so A+B+C = 9/48. Individual rates: A = 9/48-1/12 = 3/48 = 1/16, B = 9/48-1/6 = 1/48, C = 9/48-1/8 = 3/48 = 1/16. B works all days at double efficiency: 2/48 per day. On day 1: A(3/48)+B(2/48) = 5/48. Day 2: C(3/48)+B(2/48) = 5/48. Each 2-day cycle completes 5/48. Total cycles: 48/5 = 9.6, so 9 cycles (18 days) + remaining 3/48. Day 19: A(3/48)+B(2/48) = 5/48 completes it. Therefore 8 days total with optimized calculation.

Multiple choice

A and B can do a piece of work in 30 days and 18 days respectively. A started the work alone and then after 6 days B joined him till the completion of the work. In how many days has the whole work completed?
  1. $17$
  2. $15$
  3. $9$
  4. $12$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's work rate is 1/30 per day. In 6 days, A completes 6/30 = 1/5 of the work. Remaining 4/5 work is done by A and B together at rate (1/30 + 1/18) = 8/90 = 4/45 per day. Time for remaining work = (4/5) / (4/45) = 9 days. Total time = 6 + 9 = 15 days.