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

40 men can build a wall 200 m. long in 12 days working 8 hrs. a day. The number of days 30 men will take to build a similar wall 300 m. long working 6 hrs. a day will be -

  1. 36

  2. 9

  3. 32

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work = men × days × hours. For first case: 200m wall needs 40 × 12 × 8 = 3840 man-hours. So 1m needs 3840/200 = 19.2 man-hours. For 300m wall: needs 300 × 19.2 = 5760 man-hours. With 30 men working 6 hours: days = 5760/(30 × 6) = 5760/180 = 32 days.

Multiple choice

2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required?

  1. 4

  2. 8

  3. 6

  4. Cannot be determined

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

2 men's 1 day work = 1/6, so 1 man's 1 day work = 1/12. 2 women's 1 day work = 1/9, so 1 woman's 1 day work = 1/18. 3 children's 1 day work = 1/8, so 1 child's 1 day work = 1/24. Work done by 3 women + 4 children in 1 day = 3/18 + 4/24 = 1/6 + 1/6 = 1/3. Remaining work = 2/3. To finish 2/3 work in 1 day, men needed = (2/3)/(1/12) = 8. The key is finding individual work rates first.

Multiple choice

16 men can complete a work in 12 days. They worked for 4 days. To finish the remaining work in 4 days, how many additional men are required?

  1. 12

  2. 16

  3. 18

  4. 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

16 men × 12 days = 192 man-days of work. In 4 days, 16 men complete 16×4 = 64 man-days. Remaining work = 192-64 = 128 man-days. To finish in 4 days: 128/4 = 32 men needed. Additional men = 32-16 = 16. Use the man-days formula: men × days = constant work.

Multiple choice

A,B and C together complete a work in 3 days. If A or B alone completes that work in 8 days, in what time will C alone complete the same work?

  1. 12 days

  2. 5 days

  3. 2 days

  4. 24 days

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

Let total work = LCM(3, 8) = 24 units. Combined rate of A, B, C = 24/3 = 8 units/day. Rate of A alone = 24/8 = 3 units/day (same as B). Combined rate of A and B = 3 + 3 = 6 units/day. Therefore, C's rate = 8 - 6 = 2 units/day. Time for C alone = 24/2 = 12 days. The distractor 24 days comes from incorrectly adding rates instead of subtracting.

Multiple choice

15 persons complete a work in 25 days working 9 hours daily. In how many days will 25 persons complete that working 5 hours daily?

  1. 27 days

  2. 25 days

  3. 20 days

  4. 24 days

  5. 30 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is an inverse proportion problem. Total work = 15 × 25 × 9 = 3375 person-hours. For 25 persons working 5 hours daily: days = 3375 ÷ (25 × 5) = 3375 ÷ 125 = 27 days. As number of persons increases, days decrease (inverse proportion), and as hours decrease, days increase (inverse proportion).

Multiple choice

A and B can finish a work in 15 days B and C can finish the same work in 12 days and C and A in 20 days. If A, B and C start working alternately starting with A then in how many days work will finish?

  1. 10 days

  2. 30 days

  3. 15 days

  4. 5 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work = LCM(15, 12, 20) = 60 units. (A+B) = 60/15 = 4 units/day, (B+C) = 60/12 = 5 units/day, (C+A) = 60/20 = 3 units/day. Adding: 2(A+B+C) = 12, so A+B+C = 6 units/day. Individual rates: A = 6-5 = 1, B = 6-3 = 3, C = 6-4 = 2 units/day. Working alternately A→B→C: Cycle of 3 days = 1+3+2 = 6 units. 10 cycles (30 days) = 60 units, so work completes in exactly 30 days.

Multiple choice

33 men can complete work in 30 days. If 44 men started the same work together and after every day of the work, one person leaves, then in how many days will the work finish?
  1. $21$
  2. $42$
  3. $45$
  4. $44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 33 × 30 = 990 man-days. On day 1: 44 men work, completing 44 man-days. On day 2: 43 men work, completing 43 man-days. This forms an arithmetic series: 44 + 43 + 42 + ... + (44-n+1). We need sum = 990. The sum from 44 to 1 is 44×45/2 = 990 man-days. This takes 44 days (from 44 men down to 1 man).

Multiple choice

A can do a work in 60 days. He worked for 15 days and B did the remaining work in 30 days. In how many days will they do that work?

  1. 24 days

  2. 25 days

  3. 30 days

  4. 32 days

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

A's work rate = 1/60 per day. In 15 days, A completes 15/60 = 1/4 of work. Remaining work = 3/4. B does 3/4 work in 30 days, so B's rate = (3/4)/30 = 1/40 per day. Combined rate = 1/60 + 1/40 = 5/120 = 1/24 per day. Together they take 24 days. Option A is correct.

Multiple choice

A contractor under takes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one third of a road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?

  1. 75 men

  2. 100 men

  3. 65 men

  4. 46 men
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In 24 days, 25 men complete 1/3 of the work. So 25 men × 24 days = 600 man-days for 1/3 work, meaning total work = 1800 man-days. Remaining work = 1200 man-days. Time remaining = 40 - 24 - 4 = 12 days (4 days earlier than scheduled). Men needed = 1200/12 = 100 men. Extra men = 100 - 25 = 75 men. This follows the chain rule: men × days is proportional to work.

Multiple choice

2 men and 4 boys can do a piece of work in 10 days, while 4 men and 5 boys can do it in 6 days. Men and boys are paid wages according to their output. If the daily wage of a man is Rs 40, then the ratio of daily wages of a man and a boy will be -

  1. 5 : 3

  2. 5 : 2

  3. 7 : 4

  4. 7 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let m be man's work per day, b be boy's work per day. From given: 2m + 4b = 1/10 and 4m + 5b = 1/6. Solving gives m = 1/70, b = 1/140. So a man does twice the work of a boy. If man's wage is Rs 40, boy's wage should be Rs 20 (since wages are proportional to output). Ratio = 40:20 = 5:2. Common mistake is not solving the equations correctly.