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, working 8 hours a day, can do a piece of work in 20 days and 30 days, respectively. On weekends, they work for only 1 hour and on weekdays, they work for 4 hours. If they start working together on Sunday, then on which day will they finish the task? (Assume that weekend includes Saturday and Sunday)

  1. Sunday

  2. Monday

  3. Tuesday

  4. Wednesday

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

A works 4h/day weekdays, 1h/day weekends. Total work 8h/day for 20 days = 160h. A's rate = 1/160 per hour. B's rate = 1/240 per hour. Combined rate = 1/160 + 1/240 = 5/480 = 1/96 per hour. They work 4h/day weekdays and 1h/day weekends. Weekly work = 5*4 + 2*1 = 22 hours. Total work needed = 96 hours. 4 weeks = 88 hours. Remaining 8 hours finished on Tuesday.

Multiple choice

A and B work together for 8 days to complete a piece of work and B and C work together for 12 days to complete the same work. C alone can complete the work in 24 days and A is twice as efficient as B. How much time does it take to complete the work if all the three work together?

  1. 8 days

  2. 6 days

  3. 15 days

  4. 16 days

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

A+B = 1/8, B+C = 1/12, C = 1/24. B = 1/12 - 1/24 = 1/24. A = 2 * B = 2/24 = 1/12. A+B+C = 1/12 + 1/24 + 1/24 = 2/24 + 1/24 + 1/24 = 4/24 = 1/6. Time = 6 days.

Multiple choice

If four women can dig a pit in 60 days and a woman works half as much as a man, then working together, eight women and six men can dig the same pit in

  1. 6 days

  2. 8 days

  3. 5 days

  4. 12 days

  5. 16 5 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let a woman's work rate be w. Then a man's rate is 2w. Four women do the pit in 60 days, so the total work is 4w * 60 = 240w. Eight women and six men have a combined rate of 8w + 6(2w) = 20w. The time taken is 240w / 20w = 12 days.

Multiple choice

Ram, Karan and Vineet take a contract to build a house. Ram can build the house alone in 10 days. Similarly, Karan and Vineet can build the house alone in 20 and 40 days, respectively. They start the work alternately. It means that on the 1st day, only Ram works, on the 2nd day, only Karan works and on the 3rd day, only Vineet works, and so on till the work is finished. Find the total time taken by them to build the house.

  1. 16 days

  2. 15.5 days

  3. 17 days

  4. 16.5 days

  5. 17 1 7 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Ram's rate = 1/10, Karan = 1/20, Vineet = 1/40. In 3 days, they do 1/10 + 1/20 + 1/40 = 7/40. In 6 cycles (18 days), they do 42/40 (too much). In 5 cycles (15 days), they do 35/40. Remaining work = 5/40 = 1/8. Day 16: Ram does 1/10. Remaining = 1/8 - 1/10 = 1/40. Day 17: Karan does 1/20. He finishes the 1/40 in half a day. Total = 16.5 days.

Multiple choice

5 men and 2 boys started working together to complete a work which they can complete in 10 days. After 6 days, they were joined by 4 more boys. In how many days will the remaining work be completed? Statements: A. Working together, a man and a boy can complete the whole work in 40 days. B. Remaining work is done by 5 men and 6 boys. C. Working alone, 6 men could have completed half of the remaining work in 2 days.

  1. Only A is sufficient

  2. Only B is sufficient

  3. Only C is sufficient

  4. Either A or C is sufficient

  5. Either B or C is sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A gives the work rate of 1 man and 1 boy. Statement C gives the work rate of 6 men. Both allow calculating the individual rates of men and boys, which is sufficient to determine the remaining work time. Statement B is just a description of the remaining work.

Multiple choice

Ramesh and Ganesh can together complete a work in 16 days. After seven days of working together, Ramesh got sick and his efficiency fell by 30%. As a result, they completed the work in 17 days instead of 16 days. If Ganesh had worked alone after Ramesh got sick, in how many days would be have completed the remaining work?

  1. 11

  2. 12

  3. 13.5

  4. 14.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R and G be daily work rates. R+G = 1/16. In 7 days, they do 7/16 work. Remaining work = 9/16. After 7 days, R's rate becomes 0.7R. They finish in 10 more days (17-7). So, 10(0.7R + G) = 9/16. 7R + 10G = 9/16. Solving the system: R+G=1/16 => 7R+7G=7/16. Subtracting gives 3G = 2/16, so G = 2/48 = 1/24. Remaining work 9/16 divided by G (1/24) = (9/16) * 24 = 216/16 = 13.5 days.

Multiple choice

A and B can do a piece of work in 10 days and 20 days, respectively. If they work on alternate days, then find the least number of days in which the work will be completed.

  1. 13

  2. 14

  3. 12

  4. 18

  5. 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A does 1/10 of the work per day, and B does 1/20. In a 2-day cycle, they complete 1/10 + 1/20 = 3/20 of the work. After 6 cycles (12 days), 18/20 of the work is done; on day 13, A completes the remaining 2/20 (1/10) of the work.

Multiple choice

A and B work together and complete a piece of work in 24 days. They get some money for their work. If they distribute that money according to their work, A will get 50% more money than B will. In how many days can B alone complete the same work?

  1. 40

  2. 48

  3. 50

  4. 60

  5. 72
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A+B complete work in 24 days. A gets 50% more than B, so A's efficiency is 1.5 times B's. A = 1.5B. (1.5B + B) * 24 = Total Work. 2.5B * 24 = 60B. B alone takes 60 days.

Multiple choice

Directions: Study the following information carefully and answer the question that follows. Sonu can do a work in 15 days and Monu can do it in 18 days. However, together with Saif, they can do the work in 6 days. How long will Saif take to finish the work alone?

  1. 17 days

  2. 17.5 days

  3. 22.5 days

  4. 19.5 days

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

Sonu's rate = 1/15, Monu's rate = 1/18. Let Saif's rate be 1/x. Together they do 1/6 of the work per day. 1/15 + 1/18 + 1/x = 1/6. (6+5)/90 + 1/x = 1/6. 11/90 + 1/x = 15/90. 1/x = 4/90 = 2/45. x = 22.5 days.

Multiple choice

A, B and C can complete a work in 10, 12 and 15 days, respectively. All three of them start together; but after two days, A leaves the job. Also, B leaves the job 3 days before the work is completed. C completes the remaining work alone. In how many days is the total work completed?

  1. 5

  2. 6

  3. 7

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

Let total days be T. A works 2 days (2/10), B works (T-3) days (T-3)/12, C works T days (T/15). 2/10 + (T-3)/12 + T/15 = 1. Multiply by 60: 12 + 5(T-3) + 4T = 60. 12 + 5T - 15 + 4T = 60. 9T - 3 = 60. 9T = 63. T = 7.