Time and Work problems
- 1. X can do a piece of work in 40 days. He works at it for 8 days and then Y finished it in 16 days. How long will they together take to complete the work?
Options- A.
13 1 days 3 - B. 15 days
- C. 20 days
- D. 26 days Discuss
Correct Answer:
| 13 | 1 | days |
| 3 |
Explanation:
| Work done by X in 8 days = | ❨ | 1 | x 8 | ❩ | = | 1 | . |
| 40 | 5 |
| Remaining work = | ❨ | 1 - | 1 | ❩ | = | 4 | . |
| 5 | 5 |
| Now, | 4 | work is done by Y in 16 days. |
| 5 |
| Whole work will be done by Y in | ❨ | 16 x | 5 | ❩ | = 20 days. |
| 4 |
| ∴ X's 1 day's work = | 1 | , Y's 1 day's work = | 1 | . |
| 40 | 20 |
| (X + Y)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 3 | . |
| 40 | 20 | 40 |
| Hence, X and Y will together complete the work in | ❨ | 40 | ❩ | = 13 | 1 | days. |
| 3 | 3 |
- 2. A and B can do a job together in 7 days. A is 1¾ times as efficient as B. The same job can be done by A alone in :
Options- A.
9 1 days 3 - B. 11 days
- C.
12 1 days 4 - D.
16 1 days 3
Discuss
Correct Answer: 11 days
Explanation:
| (A's 1 day's work) : (B's 1 day's work) = | 7 | : 1 = 7 : 4. |
| 4 |
Let A's and B's 1 day's work be 7x and 4x respectively.
| Then, 7x + 4x = | 1 | ⟹ 11x = | 1 | ⟹ x = | 1 | . |
| 7 | 7 | 77 |
| ∴ A's 1 day's work = | ❨ | 1 | x 7 | ❩ | = | 1 | . |
| 77 | 11 |
- 3. A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Options- A.
9 1 days 5 - B.
9 2 days 5 - C.
9 3 days 5 - D. 10 Discuss
Correct Answer:
| 9 | 3 | days |
| 5 |
Explanation:
| (A + B + C)'s 1 day's work = | 1 | , |
| 4 |
| A's 1 day's work = | 1 | , |
| 16 |
| B's 1 day's work = | 1 | . |
| 12 |
| ∴ C's 1 day's work = | 1 | - | ❨ | 1 | + | 1 | ❩ | = | ❨ | 1 | - | 7 | ❩ | = | 5 | . |
| 4 | 16 | 12 | 4 | 48 | 48 |
| So, C alone can do the work in | 48 | = 9 | 3 | days. |
| 5 | 5 |
- 4. A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days B had to leave and A alone completed the remaining work. The whole work was completed in :
Options- A. 8 days
- B. 10 days
- C. 12 days
- D. 15 days Discuss
Correct Answer: 12 days
Explanation:
| (A + B)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 1 | . |
| 15 | 10 | 6 |
| Work done by A and B in 2 days = | ❨ | 1 | x 2 | ❩ | = | 1 | . |
| 6 | 3 |
| Remaining work = | ❨ | 1 - | 1 | ❩ | = | 2 | . |
| 3 | 3 |
| Now, | 1 | work is done by A in 1 day. |
| 15 |
| ∴ | 2 | work will be done by a in | ❨ | 15 x | 2 | ❩ | = 10 days. |
| 3 | 3 |
Hence, the total time taken = (10 + 2) = 12 days.
- 5. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
Options- A. 12 days
- B. 15 days
- C. 16 days
- D. 18 days Discuss
Correct Answer: 15 days
Explanation:
| A's 2 day's work = | ❨ | 1 | x 2 | ❩ | = | 1 | . |
| 20 | 10 |
| (A + B + C)'s 1 day's work = | ❨ | 1 | + | 1 | + | 1 | ❩ | = | 6 | = | 1 | . |
| 20 | 30 | 60 | 60 | 10 |
| Work done in 3 days = | ❨ | 1 | + | 1 | ❩ | = | 1 | . |
| 10 | 10 | 5 |
| Now, | 1 | work is done in 3 days. |
| 5 |
∴ Whole work will be done in (3 x 5) = 15 days.
- 6. A and B can do a piece of work in 30 days, while B and C can do the same work in 24 days and C and A in 20 days. They all work together for 10 days when B and C leave. How many days more will A take to finish the work?
Options- A. 18 days
- B. 24 days
- C. 30 days
- D. 36 days Discuss
Correct Answer: 18 days
Explanation:
| 2(A + B + C)'s 1 day's work = | ❨ | 1 | + | 1 | + | 1 | ❩ | = | 15 | = | 1 | . |
| 30 | 24 | 20 | 120 | 8 |
| Therefore, (A + B + C)'s 1 day's work = | 1 | = | 1 | . |
| 2 x 8 | 16 |
| Work done by A, B, C in 10 days = | 10 | = | 5 | . |
| 16 | 8 |
| Remaining work = | ❨ | 1 - | 5 | ❩ | = | 3 | . |
| 8 | 8 |
| A's 1 day's work = | ❨ | 1 | - | 1 | ❩ | = | 1 | . |
| 16 | 24 | 48 |
| Now, | 1 | work is done by A in 1 day. |
| 48 |
| So, | 3 | work will be done by A in | ❨ | 48 x | 3 | ❩ | = 18 days. |
| 8 | 8 |
- 7. 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Options- A. 35
- B. 40
- C. 45
- D. 50 Discuss
Correct Answer: 40
Explanation:
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y.
| Then, 4x + 6y = | 1 | and 3x + 7y = | 1 | . |
| 8 | 10 |
| Solving the two equations, we get: x = | 11 | , y = | 1 |
| 400 | 400 |
| ∴ 1 woman's 1 day's work = | 1 | . |
| 400 |
| ⟹ 10 women's 1 day's work = | ❨ | 1 | x 10 | ❩ | = | 1 | . |
| 400 | 40 |
Hence, 10 women will complete the work in 40 days.
- 8. P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?
Options- A.
5 5 11 - B.
5 6 11 - C.
6 5 11 - D.
6 6 11
Discuss
Correct Answer:
| 5 | 5 |
| 11 |
Explanation:
P can complete the work in (12 x 8) hrs. = 96 hrs.
Q can complete the work in (8 x 10) hrs. = 80 hrs.
| ∴ P's1 hour's work = | 1 | and Q's 1 hour's work = | 1 | . |
| 96 | 80 |
| (P + Q)'s 1 hour's work = | ❨ | 1 | + | 1 | ❩ | = | 11 | . |
| 96 | 80 | 480 |
| So, both P and Q will finish the work in | ❨ | 480 | ❩ | hrs. |
| 11 |
| ∴ Number of days of 8 hours each = | ❨ | 480 | x | 1 | ❩ | = | 60 | days = 5 | 5 | days. |
| 11 | 8 | 11 | 11 |
- 9. Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
Options- A. 7 hours 30 minutes
- B. 8 hours
- C. 8 hours 15 minutes
- D. 8 hours 25 minutes Discuss
Correct Answer: 8 hours 15 minutes
Explanation:
| Number of pages typed by Ravi in 1 hour = | 32 | = | 16 | . |
| 6 | 3 |
| Number of pages typed by Kumar in 1 hour = | 40 | = 8. |
| 5 |
| Number of pages typed by both in 1 hour = | ❨ | 16 | + 8 | ❩ | = | 40 | . |
| 3 | 3 |
| ∴ Time taken by both to type 110 pages = | ❨ | 110 x | 3 | ❩ | hours |
| 40 |
| = 8 | 1 | hours (or) 8 hours 15 minutes. |
| 4 |
- 10. A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
Options- A. 15 days
- B. 20 days
- C. 25 days
- D. 30 days Discuss
Correct Answer: 25 days
Explanation:
| (A + B)'s 1 day's work = | 1 |
| 10 |
| C's 1 day's work = | 1 |
| 50 |
| (A + B + C)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 6 | = | 3 | . .... (i) |
| 10 | 50 | 50 | 25 |
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
| From (i) and (ii), we get: 2 x (A's 1 day's work) = | 3 |
| 25 |
| ⟹ A's 1 day's work = | 3 | . |
| 50 |
| ∴ B's 1 day's work | ❨ | 1 | - | 3 | ❩ | = | 2 | = | 1 | . |
| 10 | 50 | 50 | 25 |
So, B alone could do the work in 25 days.
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