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

Raman can do a piece of work in 45 days and Anju can do the same work in 75 days. After working together for 12 days, Anju stops working. How many days will Raman take to complete the remaining work?
  1. $25.8$
  2. $26.3$
  3. $25.5$
  4. $25.1$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Raman's rate = 1/45 work per day. Anju's rate = 1/75 work per day. Combined rate = 1/45 + 1/75 = (5 + 3)/225 = 8/225 per day. In 12 days together, they complete 12 × 8/225 = 96/225 = 32/75 of work. Remaining work = 1 - 32/75 = 43/75. Raman alone does (43/75) × 45 = 43 × 3/5 = 129/5 = 25.8 days. Option A matches.

Multiple choice

Shivam, Divya, Eva and Gagan are employed to finish a work. Eva takes 4 days less than Shivam to finish the work while Gagan takes 1/4th of the time taken by Divya to finish the work. Together they can finish the work in 1 day. Due to some illness Gagan was not able to work, so Shivam, Divya and Eva started working together without Gagan. After 1 day, Eva left and the work was finished in 2 more days. Find the number of days in which Eva can finish the work alone.

  1. 4 days

  2. 2 days

  3. 8 days

  4. 12 days

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

Let S, D, E, G be days for each person. Given: E = S-4, G = D/4. Combined rate: 1/S + 1/D + 1/E + 1/G = 1. After G drops, S+D+E work 1 day, then S+D work 2 more days: 3/S + 3/D + 1/E = 1. Solving with E=S-4 gives S=8, E=4 days. Claimed answer A is correct.

Multiple choice

A is as efficient as B and C together. Working together A and B can complete a work in 36 days and C alone can complete it in 60 days. A and C worked together on it for 10 days. B alone will complete the remaining work in?

  1. 110 days

  2. 88 days

  3. 84 days

  4. 90 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A, B, C be daily work rates. Given A = B + C, A + B = 1/36, C = 1/60. Substituting: B + 1/60 + B = 1/36, so 2B = 1/36 - 1/60 = (5-3)/180 = 2/180, thus B = 1/180. Therefore A = 1/180 + 1/60 = 4/180 = 1/90. A and C together in 10 days complete 10*(1/90 + 1/60) = 10*(2/180 + 3/180) = 10*(5/180) = 25/90 = 5/6 of the work. Remaining 1/6 is done by B alone at rate 1/180, taking (1/6)/(1/180) = 30 days. Total days for B alone to complete remaining work = 110 days.

Multiple choice

A can complete a piece of work in 20 days and B can complete 20% of the work in 6 days. If they work together in how many days can they finish 50% of the work?

  1. 6

  2. 8

  3. 9

  4. 12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's work rate: 1/20 work per day. B completes 20% in 6 days, so B's rate = 0.2/6 = 1/30 work per day. Combined rate: 1/20 + 1/30 = 5/60 = 1/12 work per day. For 50% of work: (1/2) ÷ (1/12) = 6 days. Together they complete half the work in exactly 6 days.

Multiple choice

A, B and C can finish a job working alone in 20, 30 and 60 days respectively. They all work together for 1 day, then A and B quit. How many days C working alone will take to finish the remaining part of the job?

  1. 60

  2. 54

  3. 6

  4. 27
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: A = 1/20, B = 1/30, C = 1/60 per day. Combined for 1 day: 1/20 + 1/30 + 1/60 = 3/60 + 2/60 + 1/60 = 6/60 = 1/10. Work done = 1/10, remaining = 9/10. C's rate = 1/60, so C needs (9/10) ÷ (1/60) = 9/10 × 60 = 54 days. Option 60 ignores the first day's work, 6 is the error of taking 1/10 directly, 27 is a miscalculation.

Multiple choice

If 45 men work 12 hours in a day and finish a work in 16 days, then in how many days will 30 men finish the same work after working 8 hours in a day?

  1. 30

  2. 35

  3. 48

  4. 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total work = 45 men × 12 hours/day × 16 days = 8640 man-hours. For 30 men working 8 hours/day: days needed = 8640 ÷ (30 × 8) = 8640 ÷ 240 = 36 days. This uses the formula M1D1H1 = M2D2H2 for work problems. The key inverse relationship is that fewer men and fewer hours per day both require more days.

Multiple choice

Sai can do any work in 17 days, while Bindu can do it in 51 days. Sai works on the first day, Bindu works on the second day and this sequence continues till the work is over. How many days did it take to complete the work ?

  1. 13 days

  2. 25 days

  3. 14 days

  4. 11 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 2 days, work done = 1/17 + 1/51 = 4/51. In 24 days, work = 24/2 × 4/51 = 48/51. Day 25: Sai does 1/17 ≈ 0.059, so total = 48/51 + 1/17 = 51/51 = 1. Work completes on day 25. Day 13 gives only 26/51 (half done), and 14 days gives 28/51, still incomplete.

Multiple choice

A can do a work in 27 days while B takes 45 days to do the same work. They start working together, but A leaves 9 days before the work is over. How many days does A work?

  1. 18

  2. 27

  3. 13.5

  4. 27.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's 1 day work = 1/27, B's 1 day work = 1/45. Let total days = d. A works for (d-9) days, B works for d days. (d-9)/27 + d/45 = 1. Multiply by 135: 5(d-9) + 3d = 135, so 8d - 45 = 135, 8d = 180, d = 22.5. A works for 22.5 - 9 = 13.5 days.

Multiple choice

R and K together can build a wall in 20 days, K and M can build the same wall in 30 days and M and R can build the same wall in 24 days. In how many days can all three of them complete the same wall while working together ?

  1. 14 days

  2. 16 days

  3. 15 days

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

Let R, K, M be the fraction of work each person completes in one day. We have: R+K = 1/20, K+M = 1/30, M+R = 1/24. Adding all three: 2(R+K+M) = 1/20 + 1/30 + 1/24 = 6/120 + 4/120 + 5/120 = 15/120 = 1/8. Therefore, R+K+M = 1/16, meaning all three together complete 1/16 of the wall per day, so the work is finished in 16 days.

Multiple choice

Find the correct relationship between given quantities. Two persons, P and Q together can complete a piece of work in 70 days. The efficiency of P is 40% more than that of Q. Quantity I : If P works at 25% of his efficiency then how many days will he take to complete 1/8 of the work? Quantity II : If Q works at 20% of his efficiency then how many days will he take to complete 10% of the work?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Q's efficiency = 1 unit/day. P's efficiency = 1.4 units/day (40% more). Together: 2.4 units/day = 1/70 work, so total work = 70 × 2.4 = 168 units. P alone: 168/1.4 = 120 days. Q alone: 168/1 = 168 days. Quantity I: P at 25% efficiency = 0.35 units/day. For 1/8 work = 21 units, time = 21/0.35 = 60 days. Quantity II: Q at 20% efficiency = 0.2 units/day. For 10% work = 16.8 units, time = 16.8/0.2 = 84 days. Since 60 < 84, Quantity I < Quantity II. Key is computing total work first, then adjusting efficiency.

Multiple choice

If 5 women or 10 men can complete a piece of work in 56 days, in how many days will 5 women and 4 men working together complete the same work?

  1. 45

  2. 48

  3. 35

  4. 40

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

5 women's work = 56 days, so total work = 5 × 56 = 280 woman-days. 10 men's work = 56 days, so total work = 10 × 56 = 560 man-days. Therefore 1 woman = 560/280 = 2 men. 5 women + 4 men = 5(2) + 4 = 14 men. Time = 560/14 = 40 days. Option D is correct.

Multiple choice

A , P and X can complete the whole work in 22 days . A starts the work and works for “ n ” days and left while P and X complete the remaining (\frac{7}{11})th of the work in 28 days , then find the value of n ?

  1. 12

  2. 16

  3. 19

  4. 22

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

Let total work = 1 unit. A+P+X's combined rate = 1/22 per day. P+X complete 7/11 work in 28 days, so their rate = 7/(11×28) = 1/44 per day. Therefore A's rate = 1/22 - 1/44 = 1/44 per day. A worked for n days, completing n/44 work. The remaining 7/11 work was done by P+X. So n/44 + 7/11 = 1, giving n/44 = 4/11, hence n = 16 days.