Time and Work problems are an essential part of aptitude tests, focusing on calculating the time taken to complete a task based on the work rate of individuals or groups. These problems involve understanding concepts of work efficiency, combined work, and the distribution of tasks. Mastery of these concepts is crucial for project planning, resource allocation, and efficiency optimization.

## 1. If A can do a piece of work in 5 days, and B can do it in 10 days, how long will they take to do it together?

a) 2 days

b) 3 1/3 days

c) 5 days

d) 7 1/2 days

### Answer:

b) 3 1/3 days

### Explanation:

```
Work done by A in 1 day = 1/5, by B = 1/10.
Work done by both in 1 day = 1/5 + 1/10 = 3/10.
Together, they will take 10/3 days = 3 1/3 days.
```

## 2. A and B can complete a task in 15 days and 10 days respectively. They start working together but after 2 days, A leaves. How long will B take to complete the remaining work?

a) 6 days

b) 7 days

c) 8 days

d) 9 days

### Answer:

c) 8 days

### Explanation:

```
Work done by A and B in 1 day = 1/15 + 1/10 = 1/6.
Work done in 2 days = 2 × 1/6 = 1/3.
Remaining work = 1 - 1/3 = 2/3.
B's rate is 1/10, so time = (2/3) / (1/10) = 20/3 = 6 2/3 days.
```

## 3. A, B, and C can do a job in 20, 30, and 60 days respectively. In how many days can A do the job if he is assisted by B and C on every third day?

a) 15 days

b) 18 days

c) 20 days

d) 24 days

### Answer:

a) 15 days

### Explanation:

```
A's 1 day work = 1/20, B's = 1/30, C's = 1/60.
Work done by A in 2 days = 2 × 1/20 = 1/10.
Work done by A, B, and C in 1 day = 1/20 + 1/30 + 1/60 = 1/10.
Total work done in 3 days = 1/10 + 1/10 = 1/5.
So, the work will be completed in 15 days.
```

## 4. Working 5 hours a day, A can complete a work in 10 days. B works 6 hours a day and takes 15 days. Comparing their rates of working, find the ratio of work done by A to that by B.

a) 1:1

b) 1:2

c) 2:1

d) 3:2

### Answer:

a) 1:1

### Explanation:

```
A's work rate = Work / (Hours × Days) = 1 / (5 × 10).
B's work rate = 1 / (6 × 15).
The ratio = (1/50) / (1/90) = 90/50 = 9/5 = 1.8, which is approximately 2:1.
```

## 5. A can complete a work in 16 days and B in 24 days. If they work on it together for 4 days, then what fraction of the work is left?

a) 1/4

b) 1/3

c) 2/3

d) 3/4

### Answer:

b) 1/3

### Explanation:

```
A's 1 day work = 1/16, B's = 1/24.
Work done by A and B in 1 day = 1/16 + 1/24 = 5/48.
Work done in 4 days = 4 × 5/48 = 5/12.
Remaining work = 1 - 5/12 = 7/12.
```

## 6. C can complete a work in 12 days. C and A together can complete the same work in 8 days. A alone can complete the work in how many days?

a) 18 days

b) 24 days

c) 30 days

d) 36 days

### Answer:

b) 24 days

### Explanation:

```
C's 1 day work = 1/12.
A and C's 1 day work = 1/8.
A's 1 day work = 1/8 - 1/12 = 1/24.
A alone can complete the work in 24 days.
```

## 7. A can do a piece of work in 40 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time can B alone complete the work?

a) 50 days

b) 55 days

c) 60 days

d) 70 days

### Answer:

c) 60 days

### Explanation:

```
Work done by A in 10 days = 10/40 = 1/4.
Remaining work = 1 - 1/4 = 3/4.
B completes 3/4 work in 42 days, so he completes the work in 42 / (3/4) = 56 days.
```

## 8. A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

a) 18 days

b) 27 days

c) 36 days

d) 54 days

### Answer:

b) 27 days

### Explanation:

```
A's 1 day work = 2 × B's.
(A + B)'s 1 day work = 1/18.
Let B's 1 day work = x.
2x + x = 1/18, x = 1/54.
A's 1 day work = 2/54 = 1/27.
A alone can finish the work in 27 days.
```

## 9. A and B can do a piece of work in 72 days, B and C in 120 days, and A and C in 90 days. In how many days can A alone finish the work?

a) 80 days

b) 100 days

c) 120 days

d) 140 days

### Answer:

c) 120 days

### Explanation:

```
(A + B)'s 1 day work = 1/72, (B + C)'s = 1/120, (A + C)'s = 1/90.
Adding all, 2(A + B + C)'s work = 1/72 + 1/120 + 1/90 = 1/40.
A's 1 day work = 1/40 - 1/120 = 1/60.
A alone can finish the work in 60 days.
```

## 10. A, B, and C can complete a work in 20, 30, and 60 days respectively. If they work together, in how many days can the work be completed?

a) 10 days

b) 12 days

c) 15 days

d) 18 days

### Answer:

b) 12 days

### Explanation:

```
A's 1 day work = 1/20, B's = 1/30, C's = 1/60.
(A + B + C)'s 1 day work = 1/20 + 1/30 + 1/60 = 1/12.
Together, they can complete the work in 12 days.
```

## 11. B is 50% more efficient than A. If A alone can complete a work in 30 days, in how many days can B alone complete the work?

a) 15 days

b) 18 days

c) 20 days

d) 25 days

### Answer:

c) 20 days

### Explanation:

```
Let A's 1 day work = x.
B's 1 day work = 1.5x.
A completes the work in 30 days, so x = 1/30.
B's 1 day work = 1.5 × 1/30 = 1/20.
B alone can complete the work in 20 days.
```

## 12. A and B can do a piece of work in 6 days and 9 days respectively. A starts the work and they work alternate days. In how many days will the work be completed?

a) 7 days

b) 7.5 days

c) 8 days

d) 8.5 days

### Answer:

b) 7.5 days

### Explanation:

```
A's 1 day work = 1/6, B's = 1/9.
Work done in 2 days (A and B) = 1/6 + 1/9 = 5/18.
Work will be completed in 7 × 2/18 + 1/6 = 7.5 days.
```

## 13. C alone can complete a work in 12 days. C and A together can complete the same work in 4 days. A alone can complete the work in how many days?

a) 5 days

b) 6 days

c) 8 days

d) 10 days

### Answer:

b) 6 days

### Explanation:

```
C's 1 day work = 1/12, (C + A)'s 1 day work = 1/4.
A's 1 day work = 1/4 - 1/12 = 1/6.
So, A alone can complete the work in 6 days.
```

## 14. A and B undertake to do a piece of work for $600. A alone can do it in 6 days and B alone in 8 days. With the help of C, they finish it in 3 days. Find C's share.

a) $150

b) $175

c) $225

d) $250

### Answer:

c) $225

### Explanation:

```
A's 1 day work = 1/6, B's = 1/8.
(A + B + C)'s 1 day work = 1/3.
C's 1 day work = 1/3 - (1/6 + 1/8) = 1/24.
C's share = 1/24 of $600 = $25.
```

## 15. A can complete a work in 15 days and B in 20 days. They work together for 5 days and then B leaves. In how many more days will A complete the work?

a) 5 days

b) 6 days

c) 8 days

d) 9 days

### Answer:

c) 8 days

### Explanation:

```
A's 1 day work = 1/15, B's = 1/20.
Work done in 5 days = 5 × (1/15 + 1/20) = 5/6.
Remaining work = 1 - 5/6 = 1/6.
A will complete the remaining work in (1/6) / (1/15) = 8 days.
```

## 16. A, B, and C can do a job in 20 days. A and C together can do it in 25 days. How long will B take to do it alone?

a) 50 days

b) 60 days

c) 70 days

d) 80 days

### Answer:

a) 50 days

### Explanation:

```
(A + B + C)'s 1 day work = 1/20, (A + C)'s = 1/25.
B's 1 day work = 1/20 - 1/25 = 1/100.
So, B alone will take 100 days to complete the work.
```

## 17. A completes a task in 7 days and B in 8 days. If A works for 2 days and then B completes the remaining work, how long will B take?

a) 4 days

b) 5 days

c) 6 days

d) 7 days

### Answer:

b) 5 days

### Explanation:

```
A's 1 day work = 1/7, work done in 2 days = 2 × 1/7 = 2/7.
Remaining work = 1 - 2/7 = 5/7.
B will take (5/7) / (1/8) = 40/7 = 5.71 days ≈ 5 days.
```

## 18. A can do a piece of work in 30 days, which B alone can finish in 40 days. A worked at it for 5 days and then B completed it. How long did B work?

a) 25 days

b) 26 days

c) 27 days

d) 28 days

### Answer:

c) 27 days

### Explanation:

```
A's 1 day work = 1/30, work done by A in 5 days = 5/30 = 1/6.
Remaining work = 1 - 1/6 = 5/6.
B will take (5/6) / (1/40) = 33.33 days ≈ 27 days.
```

## 19. In a group of 3 people, A, B, and C, A alone can complete a task in 6 days, B in 8 days, and C in 12 days. If they work together, how long will it take to complete the task?

a) 2 days

b) 2.5 days

c) 3 days

d) 3.5 days

### Answer:

c) 3 days

### Explanation:

```
A's 1 day work = 1/6, B's = 1/8, C's = 1/12.
(A + B + C)'s 1 day work = 1/6 + 1/8 + 1/12 = 1/3.
Together, they will complete the work in 3 days.
```

## 20. A is thrice as efficient as B. Together, they can complete a work in 15 days. In how many days can B alone complete the work?

a) 30 days

b) 40 days

c) 45 days

d) 60 days

### Answer:

d) 60 days

### Explanation:

```
Let B's 1 day work = x.
Then A's 1 day work = 3x.
Together, (A + B)'s 1 day work = 4x = 1/15.
So, x = 1/60.
B alone will complete the work in 60 days.
```

## 21. A can complete a job in 20 days, and B can complete it in 30 days. They work together for 4 days, and then A leaves. B completes the remaining work alone. In total, how many days did it take to complete the work?

a) 17 days

b) 18 days

c) 19 days

d) 20 days

### Answer:

b) 18 days

### Explanation:

```
A's 1 day work = 1/20, B's = 1/30.
Work done in 4 days = 4 × (1/20 + 1/30) = 2/5.
Remaining work = 1 - 2/5 = 3/5.
B will complete the remaining work in (3/5) / (1/30) = 18 days.
```

## 22. C is half as efficient as A. B takes twice as long as A. If A, B, and C together can complete the work in 10 days, how long will A take to complete it alone?

a) 15 days

b) 20 days

c) 25 days

d) 30 days

### Answer:

b) 20 days

### Explanation:

```
Let A's 1 day work = 1/x.
Then, B's 1 day work = 1/(2x) and C's = 1/(2x).
(A + B + C)'s 1 day work = 1/x + 1/(2x) + 1/(2x) = 1/10.
Solve for x to find A's time = x = 20 days.
```

## 23. D does half the work done by E in the same time. E can do the same work in two-thirds the time taken by F. If D, E, and F together take 15 days to complete the work, how many days will F take to do it alone?

a) 30 days

b) 40 days

c) 45 days

d) 50 days

### Answer:

c) 45 days

### Explanation:

```
Let F's 1 day work = 1/x.
Then, E's 1 day work = 3/(2x) and D's = 3/(4x).
(D + E + F)'s 1 day work = 3/(4x) + 3/(2x) + 1/x = 1/15.
Solve for x to find F's time = x = 45 days.
```

## 24. Two pipes A and B can fill a tank in 20 and 30 minutes, respectively. If both pipes are opened together, how long will it take to fill the tank?

a) 10 minutes

b) 12 minutes

c) 15 minutes

d) 18 minutes

### Answer:

b) 12 minutes

### Explanation:

```
A's 1 minute work = 1/20, B's = 1/30.
(A + B)'s 1 minute work = 1/20 + 1/30 = 1/12.
Together, they will fill the tank in 12 minutes.
```

## 25. A completes 20% of a work in 8 days. With the help of B, he completes the rest of the work in 12 more days. B alone can complete the entire work in:

a) 30 days

b) 35 days

c) 40 days

d) 45 days

### Answer:

a) 30 days

### Explanation:

```
A's 8 days work = 20% of the total work.
Remaining work = 80%.
A and B complete this in 12 days.
Let the total work be 1 unit.
A's rate = 0.20/8 = 1/40 per day.
(A + B)'s rate = 0.80/12 = 1/15 per day.
B's rate = 1/15 - 1/40 = 1/30 per day.
B alone can complete the work in 30 days.
```