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

$A$ and $B$ can do a work in $10$ days. $B$ and $C$ can do the same work in $15$ days. $C$ and $A$ can complete the same work in $20$ days. In how many days can $C$ alone complete the work ?
  1. $120$ days
  2. $118$ days
  3. $115$ days
  4. $110$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be the work done per day. A+B=1/10, B+C=1/15, C+A=1/20. Adding these: 2(A+B+C) = 1/10 + 1/15 + 1/20 = (6+4+3)/60 = 13/60. So A+B+C = 13/120. C = (A+B+C) - (A+B) = 13/120 - 1/10 = 1/120. C takes 120 days.

Multiple choice

$A$ and $B$ can complete a task in $12$ days. However, $A$ had to leave a few days before the task was complete and hence it took $16$ days in all to complete task. If $A$ alone could complete the work in $21$ days, how many days before the work getting over did $A$ leave?
  1. $7$
  2. $9$
  3. $5$
  4. $0$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's rate be 1/21. Let B's rate be x. Together (A+B) = 1/12. So 1/21 + x = 1/12, x = 1/12 - 1/21 = (7-4)/84 = 3/84 = 1/28. If the task took 16 days, and A worked for (16-y) days, then (16-y)/21 + 16/28 = 1. (16-y)/21 + 4/7 = 1. (16-y)/21 = 3/7 = 9/21. 16-y = 9, so y = 7.

Multiple choice

If $12$ men and $16$ boys can do piece of work in $5$ days and if $13$ men and $24$ boys can do it in $4$ days, how long will $7$ men and $10$ boys take to do it ?
  1. $ 3\dfrac{2}{3} $ Days
  2. $ 8 \dfrac{1}{3} $ Days
  3. $ 4 \dfrac{5}{3} $ Days
  4. $ 9 \dfrac{1}{3} $ Days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let M be work of one man, B be work of one boy. 5(12M + 16B) = 1. 4(13M + 24B) = 1. 60M + 80B = 52M + 96B => 8M = 16B => M = 2B. Substitute: 5(12(2B) + 16B) = 5(40B) = 1 => 200B = 1. Work of 7M + 10B = 7(2B) + 10B = 24B. Time = 200B / 24B = 200/24 = 25/3 = 8 1/3 days.

Multiple choice

$A$ can do a piece of work in $20$ days and $B$ in $15$ days .They worked together on it for $6$ days and then, $A$ left . In how many days will $B$ finish the remaining work ?
  1. $ 2\dfrac{5}{2} $
  2. $ 3\dfrac{7}{3} $
  3. $ 2\dfrac{6}{5} $
  4. $ 4\dfrac{1}{2} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's rate = 1/20, B's rate = 1/15. Together they work for 6 days: 6 * (1/20 + 1/15) = 6 * (3/60 + 4/60) = 6 * 7/60 = 7/10. Remaining work = 3/10. B finishes this in (3/10) / (1/15) = 3/10 * 15 = 4.5 days, which is 4 1/2 days.

Multiple choice

A and B complete a piece of work in $24$ days. B and C do the same work in $36$ days; and A and B and C together finish it in $18$ days. In how many days will A and C together complete the work ?
  1. $24$ days
  2. $20$ days
  3. $14$ days
  4. $22$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work be 72 units. A+B = 3 units/day, B+C = 2 units/day, A+B+C = 4 units/day. C = (A+B+C) - (A+B) = 4 - 3 = 1 unit/day. A = (A+B+C) - (B+C) = 4 - 2 = 2 units/day. A+C = 2 + 1 = 3 units/day. Time = 72 / 3 = 24 days.

Multiple choice

A and B can do a piece of work in $40$ days, B and C in $30$ days, and C and A in $24$ days. In what time can each of them finish it by working alone?
  1. A in $20$ days, B in $150$ days, C in $20$ days
  2. A in $30$ days, B in $130$ days, C in $30$ days
  3. A in $60$ days, B in $120$ days, C in $40$ days
  4. A in $50$ days, B in $130$ days, C in $20$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rates be a, b, c. 1/a + 1/b = 1/40, 1/b + 1/c = 1/30, 1/c + 1/a = 1/24. Summing gives 2(1/a + 1/b + 1/c) = 1/40 + 1/30 + 1/24 = (3+4+5)/120 = 12/120 = 1/10. So 1/a + 1/b + 1/c = 1/20. Then 1/c = 1/20 - 1/40 = 1/40 (C=40), 1/a = 1/20 - 1/30 = 1/60 (A=60), 1/b = 1/20 - 1/24 = 1/120 (B=120).

Multiple choice

A can do $ \dfrac{1}{4} $ of a work in $5 $ days and B can do $ \dfrac{1}{3} $ of the same work in $10$ days . Find the number of days in which both working together will complete the work .
  1. $12$ days
  2. $20$ days
  3. $44$ days
  4. $18$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 1/4 work in 5 days, so A does 1 work in 20 days. B does 1/3 work in 10 days, so B does 1 work in 30 days. Combined rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12. They take 12 days.