Time and Work problems
- 1. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Options- A. 4 days
- B. 5 days
- C. 6 days
- D. 7 days Discuss
Correct Answer: 4 days
Explanation:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
| Then, 6x + 8y = | 1 | and 26x + 48y = | 1 | . |
| 10 | 2 |
| Solving these two equations, we get : x = | 1 | and y = | 1 | . |
| 100 | 200 |
| (15 men + 20 boy)'s 1 day's work = | ❨ | 15 | + | 20 | ❩ | = | 1 | . |
| 100 | 200 | 4 |
∴ 15 men and 20 boys can do the work in 4 days.
- 2. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Options- A. 15
- B. 16
- C. 18
- D. 25 Discuss
Correct Answer: 16
Explanation:
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.
Suppose Tanya takes x days to do the work.
| 5 : 4 :: 20 : x ⟹ x = | ❨ | 4 x 20 | ❩ |
| 5 |
⟹ x = 16 days.
Hence, Tanya takes 16 days to complete the work.
- 3. A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Options- A. 5
- B.
5 1 2 - C. 6
- D. 8 Discuss
Correct Answer: 6
Explanation:
| B's 10 day's work = | ❨ | 1 | x 10 | ❩ | = | 2 | . |
| 15 | 3 |
| Remaining work = | ❨ | 1 - | 2 | ❩ | = | 1 | . |
| 3 | 3 |
| Now, | 1 | work is done by A in 1 day. |
| 18 |
| ∴ | 1 | work is done by A in | ❨ | 18 x | 1 | ❩ | = 6 days. |
| 3 | 3 |
- 4. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Options- A. 30 days
- B. 40 days
- C. 60 days
- D. 70 days Discuss
Correct Answer: 60 days
Explanation:
Let A's 1 day's work = x and B's 1 day's work = y.
| Then, x + y = | 1 | and 16x + 44y = 1. |
| 30 |
| Solving these two equations, we get: x = | 1 | and y = | 1 |
| 60 | 60 |
| ∴ B's 1 day's work = | 1 | . |
| 60 |
Hence, B alone shall finish the whole work in 60 days.
- 5. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Options- A.
1 day 24 - B.
7 day 24 - C.
3 3 days 7 - D. 4 days Discuss
Correct Answer:
| 3 | 3 | days |
| 7 |
Explanation:
| Formula: If A can do a piece of work in n days, then A's 1 day's work = | 1 | . |
| n |
| (A + B + C)'s 1 day's work = | ❨ | 1 | + | 1 | + | 1 | ❩ | = | 7 | . |
| 24 | 6 | 12 | 24 |
| Formula: If A's 1 day's work = | 1 | , | then A can finish the work in n days. |
| n |
| So, all the three together will complete the job in | ❨ | 24 | ❩ days | = | 3 | 3 | days. |
| 7 | 7 |
- 6. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
Options- A. 5 days
- B. 6 days
- C. 10 days
- D.
10 1 days 2
Discuss
Correct Answer: 10 days
Explanation:
| (B + C)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 7 | . |
| 9 | 12 | 36 |
| Work done by B and C in 3 days = | ❨ | 7 | x 3 | ❩ | = | 7 | . |
| 36 | 12 |
| Remaining work = | ❨ | 1 - | 7 | ❩ | = | 5 | . |
| 12 | 12 |
| Now, | 1 | work is done by A in 1 day. |
| 24 |
| So, | 5 | work is done by A in | ❨ | 24 x | 5 | ❩ | = 10 days. |
| 12 | 12 |
- 7. A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Options- A. 8 hours
- B. 10 hours
- C. 12 hours
- D. 24 hours Discuss
Correct Answer: 12 hours
Explanation:
| A's 1 hour's work = | 1 | ; |
| 4 |
| (B + C)'s 1 hour's work = | 1 | ; |
| 3 |
| (A + C)'s 1 hour's work = | 1 | . |
| 2 |
| (A + B + C)'s 1 hour's work = | ❨ | 1 | + | 1 | ❩ | = | 7 | . |
| 4 | 3 | 12 |
| B's 1 hour's work = | ❨ | 7 | - | 1 | ❩ | = | 1 | . |
| 12 | 2 | 12 |
∴ B alone will take 12 hours to do the work.
- 8. A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Options- A. 23 days
- B. 37 days
- C. 37½
- D. 40 days Discuss
Correct Answer: 37½
Explanation:
| Whole work is done by A in | ❨ | 20 x | 5 | ❩ | = 25 days. |
| 4 |
| Now, | ❨ | 1 - | 4 | ❩ | i.e., | 1 | work is done by A and B in 3 days. |
| 5 | 5 |
Whole work will be done by A and B in (3 x 5) = 15 days.
| A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |
| 25 | 15 |
| ∴ B's 1 day's work = | ❨ | 1 | - | 1 | ❩ | = | 4 | = | 2 | . |
| 15 | 25 | 150 | 75 |
| So, B alone would do the work in | 75 | = 37 | 1 | days. |
| 2 | 2 |
- 9. A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
Options- A. 11 days
- B. 13 days
- C.
20 3 days 17 - D. None of these Discuss
Correct Answer: 13 days
Explanation:
Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.
| Then, 10 : 13 :: 23 : x ⟹ x = | ❨ | 23 x 13 | ❩ | ⟹ x = | 299 | . |
| 10 | 10 |
| A's 1 day's work = | 1 | ; |
| 23 |
| B's 1 day's work = | 10 | . |
| 299 |
| (A + B)'s 1 day's work = | ❨ | 1 | + | 10 | ❩ | = | 23 | = | 1 | . |
| 23 | 299 | 299 | 13 |
Therefore, A and B together can complete the work in 13 days.
- 10. A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work?
Options- A. 40
- B. 50
- C. 54
- D. 60 Discuss
Correct Answer: 60
Explanation:
| (A + B)'s 20 day's work = | ❨ | 1 | x 20 | ❩ | = | 2 | . |
| 30 | 3 |
| Remaining work = | ❨ | 1 - | 2 | ❩ | = | 1 | . |
| 3 | 3 |
| Now, | 1 | work is done by A in 20 days. |
| 3 |
Therefore, the whole work will be done by A in (20 x 3) = 60 days.
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