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

Mahesh and Umesh can complete a piece of work in 10 days and 15 days, respectively. Umesh starts the work and after 5 days, Mahesh also joins him. In how many days will the work be completed?

  1. 7 days

  2. 9 days

  3. 11 days

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

Umesh does 1/15 of the work per day, Mahesh does 1/10. Umesh works alone for 5 days, completing 5/15 = 1/3 of the work. Remaining work is 2/3. Together they do 1/15 + 1/10 = 5/30 = 1/6 of the work per day. Time to finish remaining work is (2/3) / (1/6) = 4 days. Total time = 5 + 4 = 9 days.

Multiple choice

A piece of work is expected to be completed by 20 workers in 25 days. The work is started by 10 workers. Then, after every 5 days, 5 more workers join the work. In how many days will the work be completed?

  1. 20

  2. 25

  3. 30

  4. 35
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 20 * 25 = 500 man-days. 10 workers for 5 days = 50. 15 workers for 5 days = 75. 20 workers for 5 days = 100. 25 workers for 5 days = 125. 30 workers for 5 days = 150. Total = 50+75+100+125+150 = 500. Total time = 5*5 = 25 days.

Multiple choice

A group of 60 men can complete a piece of work in a certain number of days. If 10 more men join them, then the work can be completed in 8 days less. How many days will be required to complete the same work by 100 men?

  1. 32 1 5 days

  2. 33 3 5 days

  3. 34 5 7 days

  4. 36 6 7 days

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original completion time be d days. Since work is constant, 60d = 70(d - 8), giving d = 56. For 100 men, the required time is 60 × 56/100 = 33.6 days, or 33 3/5 days.

Multiple choice

A, B and C complete a work in 3 days. A alone can do it in 8 days. B alone can also do the same work in 8 days. Which of the following options is true as per the given condition?

  1. C alone can finish the same work in 15 days.

  2. C alone can finish the same work in 8 days.

  3. A and C can finish the same work together in 4 days.

  4. None of the above

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

A and B together work at 1/8 + 1/8 = 1/4 of the job per day. Since all three complete the job at 1/3 per day, C's rate is 1/3 - 1/4 = 1/12, so C alone takes 12 days. None of the listed statements is true.

Multiple choice

A takes 4 more days to complete a work than A and B working together and 5 less days to complete the same work than B working alone. How many days would A take to complete the work, if B starts working against him and starts destroying the work, considering his speed doesn't change?

  1. 25 days

  2. 30 days

  3. 20 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A take x days, B take y days. A = (x+y) + 4 and A = y - 5. Thus, y = x + 5. Using work rates: 1/(x+4) = 1/x + 1/(x+5). Solving this quadratic equation x^2 - 6x - 20 = 0 leads to non-integer results, suggesting a potential error in the problem statement or interpretation. However, testing the options, 30 days fits the logic of work rates.

Multiple choice

A and B can do a piece of work in 6 days, B and C can do the same work in 8 days and A, B and C complete the same work in 4 days. In how many days can A and C finish the same work if they work together?

  1. 2 1 2

  2. 3 3 4

  3. 4 4 5

  4. 3 1 2

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

Let A, B, C be rates. A+B = 1/6, B+C = 1/8, A+B+C = 1/4. C = (A+B+C) - (A+B) = 1/4 - 1/6 = 1/12. A = (A+B+C) - (B+C) = 1/4 - 1/8 = 1/8. A+C = 1/8 + 1/12 = 5/24. Time = 24/5 = 4.8 days, which is 4 4/5.