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

Mohit started the work and left after 2 days, and the remaining work is completed by Suresh in 9 days. If Mohit left the work after 3 days, then Suresh will complete the remaining work in 6 days. In how many days Mohit and Suresh can complete the work individually?

  1. 5, 15

  2. 12, 15

  3. 10, 12

  4. 7, 14
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let Mohit's rate = 1/M work per day, Suresh's rate = 1/S work per day. Case 1: 2/M + 9/S = 1. Case 2: 3/M + 6/S = 1. Solve the simultaneous equations. Subtract: (3/M + 6/S) - (2/M + 9/S) = 0 → 1/M - 3/S = 0 → 1/M = 3/S → S = 3M. Substitute in first equation: 2/M + 9/(3M) = 1 → 2/M + 3/M = 1 → 5/M = 1 → M = 5 days, S = 15 days. This is a classic work-rate problem with changing scenarios.

Multiple choice

A can do a piece of work in 8 days while B alone can do it in 12 days. They work together for 4 days and the remaining work is completed by C alone in 2 days. They are paid Rs 7,200 for the completion of the entire work. The earnings of A, B and C, respectively, are:

  1. Rs 2400, Rs 2400 Rs 2400

  2. Rs 4000, Rs 2400 Rs 800

  3. Rs 3600, Rs 2400 Rs 1200

  4. Rs 3000, Rs 3000 Rs 1200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Payment is divided in proportion to work done. A did 4/8 = 1/2 of work, B did 4/12 = 1/3, and C did 1/6 (2 days at 1/12 per day). Ratio is 3:2:1. Dividing Rs 7200 gives Rs 3600, Rs 2400, Rs 1200.

Multiple choice

A can complete 25% of a work in 10 days, B can complete 40% of the same work in 20 days and C can complete 50% of same work in 30 days. They started work together. A and B left the work after 10 days. C completed the remaining work. What is the time taken to do the total work ?

  1. 33 days

  2. 31 days

  3. 30 days

  4. 32 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate: 25%/10 days = 2.5% per day. B's rate: 40%/20 days = 2% per day. C's rate: 50%/30 days = 1.67% per day. Work done in first 10 days (A+B+C): 10 × (2.5 + 2 + 1.67) = 10 × 6.17 = 61.7%. Remaining 38.3% done by C alone: 38.3/1.67 ≈ 22.9 days. Total ≈ 32.9 ≈ 33 days. Option A is correct.

Multiple choice

In a work, Z1, Z2 and Z3 work for 8, 10 and 15 days respectively. The daily wages of Z1, Z2 and Z3 are in the ratio 3:4:4 respectively. If they receive a total of ₹ 2,480 as wages for the work done, then what is the combined share of Z1 and Z3 in the total wages received?

  1. ₹ 2000

  2. ₹ 1680

  3. ₹ 1800

  4. ₹ 1540
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the daily wages be 3x, 4x, and 4x for Z1, Z2, Z3. Total wages = 8(3x) + 10(4x) + 15(4x) = 124x = ₹2480, so x = 20. Z1's share = 24x = ₹480, Z3's share = 60x = ₹1200. Combined share = ₹480 + ₹1200 = ₹1680.

Multiple choice

42 boys can complete a piece of work in 20 days working 8 hours per day. In how many days can 14 boys complete the same work, each boy working 12 hours per day?

  1. 39 days

  2. 40 days

  3. 41 days

  4. 42 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the work formula: boys × days × hours = constant work. 42 × 20 × 8 = 6720 total work units. For 14 boys working 12 hours daily: 14 × d × 12 = 6720, giving d = 6720/168 = 40 days. Fewer boys working longer hours balances out to the same total time.

Multiple choice

To complete a wall, X takes 50 percent more time than Y. If together they complete the wall in 15 days, then how much time will X alone take to complete it?

  1. 36.5 days

  2. 42.5 days

  3. 37.5 days

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

Let Y's time = y days, so X's time = 1.5y (50% more). Their combined rate: 1/y + 1/(1.5y) = 1/15. Solving gives 2.5/(1.5y) = 1/15, so y = 25 days for Y. Therefore X takes 1.5 × 25 = 37.5 days alone. Always convert 'more time' to a multiplier.

Multiple choice

A takes twice as much time as B and thrice as much time as C to finalise a task. Working together, they can complete the task in 8 days. The time (in days) taken by A, B and C, respectively, to complete the task is:

  1. 42,21,14

  2. 60,30,20

  3. 54,27,18

  4. 48,24,16
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If A takes twice as much time as B and thrice as much time as C, then B is twice as fast as A, and C is thrice as fast as A. Let A's efficiency = 1 unit/day, then B = 2 units/day, C = 3 units/day. Combined efficiency = 6 units/day. Together they complete in 8 days, so total work = 48 units. A alone: 48/1 = 48 days, B alone: 48/2 = 24 days, C alone: 48/3 = 16 days. The ratio 48:24:16 matches option D.

Multiple choice

If one man or two women or four boys or five girls can finish a work in 39 days, then how many days will one man, one woman, one boy and one girl together take to finish the same work?

  1. 40

  2. 10

  3. 30

  4. 20
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: 1 man = 39 days (1/39 work per day), 1 woman = 78 days (1/78), 1 boy = 156 days (1/156), 1 girl = 195 days (1/195). Combined rate = 1/39 + 1/78 + 1/156 + 1/195 = 20/780 + 10/780 + 5/780 + 4/780 = 39/780 = 1/20. Therefore, working together they complete the work in 20 days.

Multiple choice

Efficiency ratio of A, B and C is 3 : 2 : 4. If C alone can complete the work in 15 days, then in what time will A, B and C together finish (\frac{3}{4}) part of the same work?

  1. 4 days

  2. 5 days

  3. 6 days

  4. 8 days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

With efficiency ratio 3:2:4 and C taking 15 days alone, total work equals 60 units. Together they complete 9 units per day (3+2+4), so 3/4 of work (45 units) takes exactly 5 days. Option A (4 days) would only complete 36 units, while options C and D exceed the required time.

Multiple choice

A can complete 3/8 part of a work in 36 days. B can complete 1/2 part of the same work in 27 days. Which of the following statement(s) is/are correct? I. A is less efficient than B. II. A and B working together can complete 11/15 part of the same work in 36 days.

  1. Neither I nor II

  2. Only I

  3. Only II

  4. Both I and II
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A completes 3/8 work in 36 days, so 1 work in 36 × 8/3 = 96 days. B completes 1/2 work in 27 days, so 1 work in 27 × 2 = 54 days. A takes 96 days, B takes 54 days, so A is less efficient (slower) - Statement I is correct. Together in 1 day: 1/96 + 1/54 = 3/288 + 5.33/288 ≈ 8.33/288. In 36 days: 36 × 8.33/288 ≈ 1.04 work, not 11/15 (0.73). So II is false. Only I is correct.

Multiple choice

5 men and 8 women can complete a work in 12 days working together, while 3 men and 7 women together can complete the same work in 15 days. In how many days will 11 women complete the same work?

  1. 12

  2. 8

  3. 6

  4. 16
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let m and w be work done by one man and one woman per day. Total work = (5m + 8w) × 12 = (3m + 7w) × 15. Solving: 60m + 96w = 45m + 105w, so 15m = 9w, meaning 5m = 3w. Total work = 11w × 12 = 132w. Therefore 11 women need 132w ÷ 11w = 12 days. Option A is correct.

Multiple choice

8 men or 10 boys can complete a work in 174 days. 12 men and 14 boys will complete the same work in how many days?

  1. 60 days

  2. 50 days

  3. 72 days

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

8 men or 10 boys can complete work in 174 days. Let 1 man's work = m units/day and 1 boy's work = b units/day. So 8m = 10b, meaning m/b = 5/4. Let m = 5 units/day, then b = 4 units/day. Total work = 8 × 5 × 174 = 3480 units. 12 men and 14 boys do 12(5) + 14(4) = 60 + 56 = 116 units/day. Days needed = 3480/116 = 30 days. Wait - let me recalculate: 8m × 174 = total work. If 8m = 1 work, then 1 work = 8m. So 8m × 174 = 1392m total work. 12m + 14(0.8m) = 12m + 11.2m = 23.2m. Days = 1392m/23.2m = 60 days.

Multiple choice

Naman does half the work as Gagan in 4/5 the time. If together they take 16 days to complete a piece of work, then how long will it take Gagan to complete the work ?

  1. 23 days

  2. 24 days

  3. 25 days

  4. 26 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Gagan's efficiency be 1 unit. Naman does half the work in 4/5 the time, so Naman's efficiency = (1/2)/(4/5) = 5/8. Combined efficiency = 1 + 5/8 = 13/8. They complete the work in 16 days, so total work = 16 × 13/8 = 26 units. Gagan alone would take 26/1 = 26 days. The key is understanding relative efficiency from the given relationship.