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 takes 25 days more than that taken by A and B together to do a work, while B takes 9 days more than that taken by A and B together to do the work. In how many days can A complete the work if he is assisted by B on every alternate day starting from the second day?

  1. 240/11 days

  2. (21 + 7/8) days

  3. 24 days

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

If A+B take T days, A takes T+25 and B takes T+9. 1/(T+25) + 1/(T+9) = 1/T. Solving gives T^2 = 225, so T = 15. A takes 40 days, B takes 24 days. Working alternate days: Day 1 (A): 1/40. Day 2 (A+B): 1/40 + 1/24 = 3/120 + 5/120 = 8/120 = 1/15. In 2 days, 1/40 + 1/15 = 11/120. In 20 days (10 cycles), 110/120 done. Remaining 10/120 = 1/12. Day 21 (A): 1/40. Remaining 1/12 - 1/40 = 7/120. Day 22 (A+B): 1/15. Remaining 7/120 - 8/120 (negative). Time is 21 + (7/120)/(8/120) = 21 + 7/8.

Multiple choice

Karan can build a wall in 20 days, while Amit can completely destroy the wall in 40 days. Kapil can build the wall twice as efficiently as Karan. If Karan, Kapil and Amit start working at the same time, then in how many days will the wall be completely built?

  1. 6 days

  2. 8 days

  3. 11 days

  4. 15 days

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

Karan rate = 1/20. Amit rate = -1/40. Kapil rate = 2 * (1/20) = 1/10. Combined rate = 1/20 + 1/10 - 1/40 = (2+4-1)/40 = 5/40 = 1/8. Time = 8 days.

Multiple choice

In one day, a man can do twice the amount of work done by a child in a day. It takes 40 days for 50 children, working 8 hours a day, to complete a piece of work. If 40 men work for 5 hours a day, then how many days will it take for them to complete the same piece of work?

  1. 40 days

  2. 60 days

  3. 80 days

  4. 10 days

  5. 120 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A man does twice the work of a child. 50 children working 8 hours for 40 days = 16000 child-units. 40 men (equivalent to 80 children) working 5 hours a day for D days: 80 * 5 * D = 400D. Setting 400D = 16000 gives D = 40.

Multiple choice

Arun can do half as much work as Bipul in three-fourth of the time. If they take 21 days to complete the work together, then how much time shall Bipul take to do the work?

  1. 32 days

  2. 35 days

  3. 37 days

  4. 39 days

  5. 42 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arun takes 3/4 time of Bipul to do half work. So Arun takes 3/2 time of Bipul to do full work. Let Bipul take x days, then Arun takes 1.5x days. 1/x + 1/1.5x = 1/21. (1.5 + 1) / 1.5x = 1/21. 2.5 / 1.5x = 1/21. 5 / 3x = 1/21. 3x = 105, so x = 35.

Multiple choice

A, B and C can do a piece of work in 8 days. A and B can do the same piece of work in 10 days, whereas B and C can do the same piece of work in 12 days. How many days will A and C take to do the same piece of work?

  1. 10 days

  2. 12 days

  3. 14 days

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

Let work be 1 unit. (A+B+C) = 1/8, (A+B) = 1/10, (B+C) = 1/12. We want (A+C). Note that (A+B) + (B+C) = A + 2B + C = 1/10 + 1/12 = 11/60. Also (A+B+C) = 1/8. So B = (A+B+C) - (A+C) is not direct. Instead, (A+B+C) - (B+C) = A = 1/8 - 1/12 = 1/24. (A+B+C) - (A+B) = C = 1/8 - 1/10 = 1/40. A+C = 1/24 + 1/40 = (5+3)/120 = 8/120 = 1/15. Thus, they take 15 days.

Multiple choice

Four women and 12 children together take 4 days to complete a piece of work. How many days will 4 children alone take to complete the piece of work if 2 women alone can complete the piece of work in 16 days?

  1. 32

  2. 24

  3. 16

  4. 12

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

If 2 women take 16 days, 1 woman takes 32 days. 4 women take 32/4 = 8 days. In 4 days, 4 women do 4/8 = 1/2 of the work. The remaining 1/2 work is done by 12 children in 4 days, so 12 children do 1/8 of the work per day. 4 children do 1/24 of the work per day, taking 24 days.

Multiple choice

If 4 men or 10 boys can do a piece of work in 12 days, working 10 hours a day, then how many days will it take to complete a piece of work thrice the previous work with 8 men and 5 boys working together for 9 hours a day?

  1. 16 days

  2. 14 days

  3. 12 days

  4. 21 days

  5. 18 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the formula (M1*D1*H1)/W1 = (M2*D2*H2)/W2, where 4 men = 10 boys, we find 1 man = 2.5 boys. The first work is 1 unit, the second is 3 units. 8 men and 5 boys equal 20 + 5 = 25 boys. Solving (10*12*10)/1 = (25*D2*9)/3 gives D2 = 16.

Multiple choice

Directions: Read the following information to answer the question given below: (x + 5) men can complete a work in (x + 3) days, and (x + 15) men can complete 50% of the same work in 2 days. What is the percent decrease in the number of days, if instead of 10 men doing the work each day, they are assisted by 15 children each day and if each child does as much work in 30 days as done by 1 man in 20 days?

  1. 25%

  2. 30%

  3. 37.5%

  4. 50%

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