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

10 men & 5 women complete a work in 12 days while 8 children can complete same work in 16 days. In how many days 3 men and 2 women & 2 children can complete the same work ?

  1. 6 days

  2. 12 days

  3. 14 days

  4. Can’t be determined

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

We know: 10 men + 5 women complete the work in 12 days. Also: 8 children complete the same work in 16 days. We need to find: 3 men + 2 women + 2 children's rate. However, we have no information about the relative efficiency of men vs women vs children. Without knowing how a man's work compares to a woman's or a child's, we cannot combine these rates. The data is insufficient.

Multiple choice

Two men undertake to do a work for Rs. 200. One alone could do it in 6 days the other in 8 days, With the assistance of a boy they finish it in 3 days. How much money should be given to the boy?

  1. Rs.25

  2. Rs. 20

  3. Rs. 45

  4. Rs. 65
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First man's rate: 1/6 work per day. Second man's rate: 1/8 work per day. Together with boy, they finish in 3 days, so combined rate is 1/3 per day. Boy's rate = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24. Boy does 3 × (1/24) = 1/8 of work. His share = (1/8) × Rs. 200 = Rs. 25. Options B (Rs. 20), C (Rs. 45), and D (Rs. 65) are incorrect.

Multiple choice

12 men can complete a work in 10 days. 20 women can complete the same work in 12 days. 8 men and 4 women started working and after 9 days 10 more women joined them. How many days will they now take to complete the remaining work?

  1. 2 days

  2. 5 days

  3. 6 days

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

12 men's rate = 1/10 work/day, so 1 man = 1/120. 20 women's rate = 1/12, so 1 woman = 1/240. 8 men + 4 women work for 9 days: (8/120 + 4/240) × 9 = (0.067 + 0.017) × 9 = 0.75 work done. Remaining = 0.25. New team: 8 men + 14 women = 8/120 + 14/240 = 0.067 + 0.058 = 0.125/day. Days needed = 0.25/0.125 = 2 days.

Multiple choice

Some staff promised to do a job in 18 days, but 6 of them went on leave, So the remaining men took 20 days to complete the job. How many men were there originally?

  1. 55

  2. 62

  3. 56

  4. 60
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original men = M. Work = M × 18 man-days. When 6 men leave, M - 6 men take 20 days: (M-6) × 20 = M × 18. Solving: 20M - 120 = 18M, so 2M = 120, giving M = 60 men originally. This uses the inverse relationship between men and time for constant work.

Multiple choice

A certain number of men can do a piece of work in 40 days. If there were 45 men more, the work could have been finished in 25 days. Find the original number of men employed in the work.

  1. 70

  2. 85

  3. 65

  4. 75
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original men = M. Work = M × 40 man-days. With 45 more men: (M + 45) × 25 = M × 40. Solving: 25M + 1125 = 40M, so 15M = 1125, giving M = 75 men originally. This follows from the inverse proportionality - more men means fewer days needed.

Multiple choice

Ram is four times as efficient as Shyam. If both can complete the work in 11 days then in how many days Shyam will complete the work ?

  1. 44 days

  2. 50 days

  3. 65 days

  4. 55 days

  5. 58 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If Ram is 4 times as efficient as Shyam, then Ram does 4 units of work per day while Shyam does 1 unit per day. Together, they do 5 units per day and complete the work in 11 days, so total work = 5 × 11 = 55 units. Shyam alone would take 55 units ÷ 1 unit/day = 55 days. This is option D.

Multiple choice

A and B can do a work in 8 days, B and C can do the same work in 12 days while A, B and C can do the same work in 6 days. In how many days will A and C do the same work?

  1. 4

  2. 6

  3. 8

  4. 12

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

Let A, B, C's 1-day work be a, b, c. From the given: a+b=1/8, b+c=1/12, a+b+c=1/6. Subtract third from first: c = 1/6 - 1/8 = 1/24. Subtract third from second: a = 1/6 - 1/12 = 1/12. Therefore, A+C together do 1/12 + 1/24 = 1/8 work per day, taking 8 days to complete.

Multiple choice

16 men does a work in 16 days 20 women does the same work in 16 days. In how many days will 8 men and 10 women do the same work?

  1. 10 days

  2. 12 days

  3. 18 days

  4. 16 days

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

16 men × 16 days = 256 man-days. 20 women × 16 days = 320 woman-days. So 16 man-days = 20 woman-days, or 4 men = 5 women. Work needed = 256 man-days. 8 men + 10 women = 8 men + 8 men = 16 men (since 10 women = 8 men). Days = 256/16 = 16 days.

Multiple choice

‘X’ and ‘Y’ can do a piece of work in 24 days and 32 days respectively. They begin together but 4 days before the completion of the work, ‘X’ leaves off. Find the total number of days for the work to be completed.

  1. 12 days

  2. 14 days

  3. 8 days

  4. 15 days

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

Let total time = T days. X works for (T-4) days at 1/24 per day, Y works for T days at 1/32 per day. Equation: (T-4)/24 + T/32 = 1. Solving: 4(T-4) + 3T = 96, giving 7T - 16 = 96, so T = 16 days. The answer should be 16 days, but since this isn't among options A-D, 'None of these' is indeed correct.

Multiple choice

36 men can do a piece of work in 16 days. They start the work, but after 4 days, 6 men are replaced by 48 women. Find the number of days in which the remaining work becomes complete if the efficiency of 1 woman is 50\% that of a man?

  1. 6 days

  2. 4 days

  3. 5 days

  4. 8 days

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

36 men complete work in 16 days, so total work = 576 man-days. After 4 days, work done = 144 man-days, remaining = 432 man-days. New team: 30 men + 48 women (where 2 women = 1 man, so 48 women = 24 man-equivalent) = 54 man-equivalent. Days needed = 432/54 = 8 days exactly. The claimed answer D (8 days) is correct.

Multiple choice

‘A’ can do a piece of work in 10 days while B alone can do it in 15 days. They work together for 5 days and the rest of work is done by ‘C’ in 24 days. If they get Rs 1614 for the whole work, what is the share of ‘C’.

  1. 350 Rs.

  2. 450 Rs.

  3. 269 Rs.

  4. 369 Rs.

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

A's rate = 1/10 per day, B's rate = 1/15 per day. Together in 5 days they complete 5(1/10+1/15) = 5(1/6) = 5/6 of work. Remaining 1/6 done by C in 24 days, so C's rate = 1/144 per day. Total rate of all three = 1/10+1/15+1/144. C's share of wage = (C's rate)/(combined rate) × 1614 = 1614/24 = 67.25. However, looking at the options, 269 Rs equals 4 × 67.25, suggesting C's work share is 1/6 of total, so wage = (1/6)/(1) × 1614 = 269. Answer C is correct.

Multiple choice

‘A’ can do a piece of work in 20 days and ‘B’ can do the same work in 12 days. Find the number of days in which they can complete the whole work if they work on alternate days and the work is started by ‘A’?
  1. $\(\frac{23}{89}\) days$
  2. $\(\frac{76}{5}\) days$
  3. $\(\frac{66}{7}\) days$
  4. $17 days$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A's work per day = 1/20, B's = 1/12. They work alternately starting with A. In 2 days, work done = 1/20 + 1/12 = 8/60 = 2/15. After 14 complete cycles (28 days), work = 28/15 ≈ 1.87 > 1, so fewer cycles needed. After 7 cycles (14 days), work = 14/15. Remaining 1/15 done by A in (1/15)/(1/20) = 4/5 days. Total = 14 + 4/5 = 76/5 days.