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

Pannalal does 1/3rd of a job in 20 days, Saiprasad completes the rest of the job in 10 days. In how many days can they together do the job?

  1. 12 days

  2. 6 days

  3. 3 days

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

Pannalal does 1/3 of the job in 20 days, so he does the whole job in 60 days. Saiprasad does the remaining 2/3 of the job in 10 days, so he does the whole job in 15 days. Their combined rate is 1/60 + 1/15 = 5/60 = 1/12, meaning they finish in 12 days.

Multiple choice

In completing a project, Jason works twice as fast as Milli. If Milli can complete a work in 12 days independently, then the number of days in which Jason and Milli can together finish the work are

  1. 2 days

  2. 3 days

  3. 4 days

  4. 5 days

  5. 6 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Milli takes 12 days, so her rate is 1/12 work/day. Jason is twice as fast, so his rate is 2/12 = 1/6 work/day. Together, their rate is 1/12 + 1/6 = 3/12 = 1/4 work/day. They finish in 4 days.

Multiple choice

R takes twice as long as A and S together take to do a certain piece of work. A takes thrice as long as S and R together. The three together can do the work in 10 days. How many days would S alone take to do the work?

  1. 40 days

  2. 30 days

  3. 16 days

  4. 24 days

  5. 20 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the daily work rates of R, A, and S be r, a, and s respectively. Since R takes twice as long as A and S together, we have r = (a + s)/2, which means the total rate r + a + s = 3r = 1/10, so r = 1/30. Similarly, since A takes thrice as long as S and R together, we have a = (s + r)/3, which means r + a + s = 4a = 1/10, so a = 1/40. Solving for s gives s = 1/10 - 1/30 - 1/40 = 1/24, meaning S alone takes 24 days.

Multiple choice

12 men and 16 women together can complete a piece of work in 4 days. If it takes 80 days for one man alone to complete the same work, then how many days would be required for one woman alone to complete the same work?

  1. 160 days

  2. 150 days

  3. 130 days

  4. 175 days

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

1 man = 1/80 work/day. 12 men = 12/80 = 3/20 work/day. Total work = 1/4 per day. 16 women = 1/4 - 3/20 = 5/20 - 3/20 = 2/20 = 1/10 per day. 1 woman = 1/(16 * 10) = 1/160 work/day. So, 160 days.

Multiple choice

P and Q can do a work in 30 days and 18 days, respectively. P started the work and after 6 days, Q joined him to complete the work. In how much time was the total work done?

  1. 15 days

  2. 12 days

  3. 10 days

  4. 9 days

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

P's rate = 1/30, Q's rate = 1/18. P works for 6 days alone: 6/30 = 1/5 work done. Remaining = 4/5. Combined rate = 1/30 + 1/18 = (3+5)/90 = 8/90 = 4/45. Time for remaining = (4/5) / (4/45) = 9 days. Total time = 6 + 9 = 15 days.

Multiple choice

A, B and C can do a work in 15 days. They started the work and after 6 days, A left. B and C finished the work in another 15 days. In how much time can A alone finish the work?

  1. 32.5 days

  2. 35 days

  3. 37.5 days

  4. 42 days

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

A, B, and C together complete 1/15 of the work per day. In 6 days, they complete 6/15 = 2/5 of the work, leaving 3/5 to be finished by B and C in 15 days, meaning B and C complete 1/25 of the work per day. Subtracting (B+C)'s rate from (A+B+C)'s rate gives A's rate: 1/15 - 1/25 = (5-3)/75 = 2/75. Thus, A takes 75/2 = 37.5 days to finish the work alone.

Multiple choice

Mayank, Deepak and Pawan, each of them working alone can complete a piece of work in 5, 10 and 15 days,respectively. If all three of them work together to complete the work and earn Rs. 11,000, what will be Deepak's share of the earnings?

  1. Rs. 2000

  2. Rs. 6000

  3. Rs. 4000

  4. Rs. 3000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: Mayank = 1/5, Deepak = 1/10, Pawan = 1/15. Ratio of work done = 1/5 : 1/10 : 1/15 = 6 : 3 : 2. Total parts = 6+3+2 = 11. Deepak's share = (3/11) * 11000 = 3000.

Multiple choice

A and B together can do a piece of work in 15 days while B and C together can do the same work in 12 days and C and A together can do the same work in 10 days. They all work together for 5 days, then B and C leave. How many more days will A take to finish the remaining work?

  1. 18

  2. 12

  3. 10

  4. 9

  5. 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A+B=1/15, B+C=1/12, C+A=1/10. 2(A+B+C) = 1/15 + 1/12 + 1/10 = (4+5+6)/60 = 15/60 = 1/4. A+B+C = 1/8. After 5 days, work done = 5/8. Remaining = 3/8. A's efficiency = (A+B+C) - (B+C) = 1/8 - 1/12 = (3-2)/24 = 1/24. Time for A = (3/8) / (1/24) = 9 days.