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

12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days.6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on job to complete the remaining work, if it is to be completed in 3 days?

  1. 15

  2. 22

  3. 18

  4. Data inadequate

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

12 men in 4 days means total work = 48 man-days. So 1 man does 1/48 of work per day. 6 men work for 2 days, completing 6 × 2 × (1/48) = 12/48 = 1/4 of work. Remaining 3/4 work must be done in 3 days. 15 women complete full work in 4 days, so 1 woman does 1/60 per day. In 3 days, 15 women do 15 × 3 × (1/60) = 45/60 = 3/4 of work. Exactly what's needed.

Multiple choice

A can do a piece of work in 18 days. If B joins A after 9 days, in how many days more will the work be completed? I. B works faster than A. II. The ratio of the measure of the amount of work done by A and B in one day is 2 : 3.

  1. The question cannot be answered even with the help of both the statements together.

  2. The question can be answered with the help of statement II alone.

  3. The question can be answered with the help of statement I alone.

  4. The question can be answered with the help of both statements together.

  5. The question can be answered with either statement I or statement II.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A completes work in 18 days, so A's rate = 1/18 per day. After 9 days, A completes 9/18 = 1/2 of work. Remaining = 1/2. Statement I: B works faster than A (insufficient). Statement II: A:B work ratio = 2:3, so B's rate = (3/2)×(1/18) = 1/12 per day. Combined rate = 1/18 + 1/12 = 5/36 per day. Time for half work = (1/2)/(5/36) = 18/5 = 3.6 days. Statement II alone is sufficient.

Multiple choice

A, B and C complete a work in 10, 12, and 15 days respectively. If they continue working together till the last, find the share of B out of the total wages of Rs. 750.

  1. 250

  2. 320

  3. 280

  4. 350
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A, B, C can complete work in 10, 12, 15 days respectively. Their work per day ratios are 1/10 : 1/12 : 1/15 = 6:5:4 (LCM method). Total parts = 6+5+4 = 15. B's share = (5/15) × 750 = 250. Wages are distributed in proportion to work contribution.

Multiple choice

A and B can do a piece of work in 20 days while B and C can do the same piece of work in 30 days and C and A can do the same piece of work in 40 days. In how many days can C alone do 30% of that work?

  1. 78

  2. 76

  3. 72

  4. 84
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A+B, B+C, C+A work rates be 1/20, 1/30, 1/40 respectively per day. Adding all: 2(A+B+C) = 1/20+1/30+1/40 = 13/120. So A+B+C = 13/240 per day. C alone = (13/240) - (1/20) = 13/240-12/240 = 1/240 per day. For 30% work: 0.3×240 = 72 days.

Multiple choice

80 men can complete a work in 30 days. They start work together and after every 10 days 10 men left the work. In how much time work will be completed?

  1. 30 days

  2. 32 days

  3. 36 days

  4. 46 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = 80 × 30 = 2400 man-days. Work completed in first 10 days with 80 men = 800 man-days. Work in next 10 days (11-20) with 70 men = 700 man-days. Work in next 10 days (21-30) with 60 men = 600 man-days. After 30 days, total work done = 2100 man-days. Remaining work = 300 man-days with 50 men, which takes 300/50 = 6 days. Total time = 30 + 6 = 36 days.

Multiple choice

A and B have been put into a work to complete it in 40 days. They work for 10 days then they are forced to work with double of their efficiencies. In total how many days work will be completed?

  1. 20 days

  2. 25 days

  3. 30 days

  4. 34 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total work = 1 unit. A and B together complete in 40 days, so their combined rate = 1/40 per day. In first 10 days, they complete 10 × (1/40) = 1/4 work. Remaining = 3/4. Now their rate doubles to 1/20 per day. Time for remaining = (3/4) ÷ (1/20) = 15 days. Total = 10 + 15 = 25 days.

Multiple choice

Pranesh can do a work in 15 days. In how many days will the work be completed by his brother Avinash if efficiency of Avinash is 60% more than that of Pranesh?

  1. 9

  2. 9.5

  3. 9.375

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

If Pranesh completes the work in 15 days, his rate is 1/15 work per day. Avinash is 60% more efficient, so his rate is (1/15) × 1.60 = 1.6/15. The time Avinash needs is the reciprocal: 15/1.6 = 9.375 days. This is calculated by dividing Pranesh's time by (1 + efficiency percentage as decimal). Option C is correct.

Multiple choice

Mohit is five times as efficient as Rohit. If Mohit can complete a piece of work in 28 days less than Rohit, then in how many days can Rohit alone complete the same work?

  1. 35 days

  2. 32 days

  3. 45 days

  4. 40 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If Mohit is 5 times as efficient as Rohit, he takes 1/5 the time to complete the same work. Let Rohit take R days. Then R - R/5 = 28, giving 4R/5 = 28, so R = 35 days. Rohit alone completes the work in 35 days. Option A is correct.

Multiple choice

A, B and C can do a piece of work in 20, 30 and 60 days respectively. How many days does it needed to complete the work if A does the work and he is assisted by B and C on every third day?

  1. 10

  2. 14

  3. 15

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A completes 1/20 of the work daily. B completes 1/30 daily, and C completes 1/60 daily. On every third day, all three work together, completing 1/20 + 1/30 + 1/60 = 6/60 = 1/10 of the work. The 3-day cycle completes 1/20 + 1/20 + 1/10 = 1/5 of the work. In 15 days (5 cycles), they complete 5 × (1/5) = 1, meaning the entire work is finished. The other options don't align with this cyclical pattern.

Multiple choice

4 men and 5 women can complete a work in 15 days, whereas 9 men and 6 women can complete the same work in 10 days, to complete the work in 7 days, how many women should assist 4 men?

  1. 11

  2. 14

  3. 15

  4. 13
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let m and w be work done by 1 man and 1 woman per day. From given: 4m + 5w = 1/15 and 9m + 6w = 1/10. Solving gives w = 2m. For 4 men and x women to finish in 7 days: 4m + x(2m) = 1/7. Substituting m = 1/210 gives x = 13 women.

Multiple choice

Which of the given statements is/are necessary/required to answer the question. Rashmi works for 4 days and leaves the work. In how many days can Rashmi alone can finish the remaining work? I-Rashmi and Sweta can complete the whole work in 80/9 days. II-When Rashmi left 25% work was done. III-Sweta is 20% less efficient than Rashmi.

  1. Only I and III

  2. All three together are sufficient

  3. All three together are not sufficient

  4. I or (II and III) are sufficient

  5. II or (I and III) are sufficient
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Rashmi worked for 4 days when 25% work was done. So remaining work = 75%. Statement I: Rashmi + Sweta complete in 80/9 days, so combined rate = 9/80 per day. Statement III: Sweta's efficiency is 20% less than Rashmi, so Sweta's rate = 0.8 × Rashmi's rate. If Rashmi's rate = r, then r + 0.8r = 9/80, so 1.8r = 9/80, r = 1/16 per day. For 75% work at rate 1/16: days = (3/4)/(1/16) = 12 days. Statements II and III are sufficient. Alternatively: I+III gives Rashmi's rate = 1/16, and we know 4 days were worked. We need to know how much work is left (from II) to calculate remaining days. So 'II or (I and III)' are sufficient. Claimed answer E is correct.

Multiple choice

Find the correct relationship between given quantities. Mahesh can complete a piece of work in 60 days whereas Kavya and Sarita working together can complete it in 15 days. When Mahesh and Sarita alternately work for a day each the work gets completed in 40 days. Quantity 1: No. of days in which Kavya will complete the work. Quantity 2: No. of days in which Sarita will complete 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 No relationship can be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Mahesh: 60 days. Kavya+Sarita: 15 days. Mahesh+Sarita (alternate days): 40 days. Let Kavya take k days, Sarita take s days. Kavya+Sarita combined rate: 1/15. Mahesh's rate: 1/60. When working alternate days, in 40 days they complete 40*(1/60 + 1/s)/2 = 40/120 + 20/s. This equals 1. So 1/3 + 20/s = 1, giving s = 30. So Sarita takes 30 days. Then Kavya takes 1/(1/15 - 1/30) = 30 days. Both take 30 days, so Kavya = Sarita, meaning Quantity I = Quantity II.

Multiple choice

To do a certain work, the ratio of efficiencies of X and Y is 5 : 4. Working together, they can complete the same work in 10 days. Y alone starts the work and leaves after 5 days. The remaining work will be completed by X alone in ?

  1. 14 days

  2. 12 days

  3. 15 days

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

Let X's efficiency = 5k, Y's efficiency = 4k. Combined efficiency = 9k. Together they complete work in 10 days, so total work = 90k. Y works alone for 5 days, completing 20k. Remaining work = 70k. X alone does 5k per day, so time needed = 70k/5k = 14 days. Option A is correct.

Multiple choice

A, B and C can complete the whole work in 12 days . C starts the work and works for z days and left , while A and B complete the remaining 7/12 th of the work in 14 days , then find the value of z ?

  1. 10

  2. 12

  3. 15

  4. 20

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

Combined work rate of A, B, C = 1/12 work per day. A and B complete 7/12 work in 14 days, so their rate = (7/12)/14 = 1/24 per day. Therefore, C's rate = (1/12 - 1/24) = 1/24 per day. C completed 5/12 work alone, so time = (5/12)/(1/24) = 10 days.