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 task was assigned to P, Q and R to be completed in not more than seven days. P alone can complete the task in ten days. Q alone can complete the task in twelve days and R alone can complete the task in fifteen days. All three of them worked for two days and P and Q together worked for another two days. What portion of the task will remain after four days?

  1. 1/10

  2. 1/5

  3. 1/6

  4. 2/15

  5. 1/8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P's rate = 1/10, Q's = 1/12, R's = 1/15. Combined rate = (6+5+4)/60 = 15/60 = 1/4. Work in 2 days = 2 * 1/4 = 1/2. P+Q rate = 1/10 + 1/12 = 11/60. Work in 2 days = 2 * 11/60 = 11/30. Total work done = 1/2 + 11/30 = 15/30 + 11/30 = 26/30 = 13/15. Remaining = 1 - 13/15 = 2/15.

Multiple choice

P, Q and R can do a piece of work in 12, 16 and 24 days, respectively. They started the work together, but P left after working for 3 days and Q left 3 days before the completion of work. In how many days was the total work completed?

  1. 6 days

  2. 8 days

  3. 12 days

  4. 9 days

  5. 11 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total days be x. P worked 3 days (3/12 work). Q worked (x-3) days. R worked x days. Equation: 3/12 + (x-3)/16 + x/24 = 1. Multiplying by 48: 12 + 3(x-3) + 2x = 48, so 12 + 3x - 9 + 2x = 48, 5x = 45, x = 9.

Multiple choice

A and B can complete a piece of work in 20 and 30 days, respectively. A and B started the work and after 10 days, A left the job and then C joined B and completed the job by taking 1 day more than the estimated time. How many days would C take to complete the work independently?

  1. 20

  2. 24

  3. 30

  4. 45

  5. 50
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A and B work for 10 days: 10 * (1/20 + 1/30) = 10 * (5/60) = 5/6. Remaining work = 1/6. B and C finish this in 1 day more than estimated. Estimated time for A+B = 1 / (1/20 + 1/30) = 12 days. They worked 10, so 2 days left. C and B finish in 2+1 = 3 days. 3 * (1/30 + 1/C) = 1/6. 1/30 + 1/C = 1/18. 1/C = 1/18 - 1/30 = (5-3)/90 = 2/90 = 1/45. C = 45 days.

Multiple choice

A is 60% more efficient than B. If A takes 9 days less than B to do a certain piece of work, then find the number of days it would take them to complete the same work, if both work together.

  1. 6 8 13 days

  2. 8 4 13 days

  3. 9 days

  4. 9 3 13 days

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

If B takes t days, A takes t/1.6 days. Their time difference is 9, so t/1.6 = 15 and t = 24. Their combined rate is 1/15 + 1/24 = 13/120, so the joint time is 120/13 = 9 3/13 days.

Multiple choice

A job can be finished by 20 men in 30 days, working 4 hours a day. If the job was assigned to 30 men who worked for 20 days at 3 hours a day, at the end of which only one was retained, how many more days will it take for the last workman to complete the remaining work, working 10 hours a day?

  1. 20

  2. 30

  3. 40

  4. 60

  5. 45
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 20 * 30 * 4 = 2400 man-hours. Work done = 30 * 20 * 3 = 1800 man-hours. Remaining work = 600 man-hours. One man working 10 hours a day takes 600 / 10 = 60 days.

Multiple choice

Sixteen women take 12 days to complete a piece of work, which can be completed by 12 men in 8 days. Sixteen men start working and after 3 days, 10 men leave and 4 women join them. How many days will it take them to complete the remaining work?

  1. 4

  2. 6

  3. 8

  4. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

16 women * 12 days = 192 woman-days. 12 men * 8 days = 96 man-days. 1 man = 2 women. 16 men start, after 3 days they do 16*3=48 man-units. Remaining = 96-48=48 man-units = 96 woman-units. New group: 6 men + 4 women = 12+4=16 women. 96/16 = 6 days.