Time and Work problems
- 1. Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
Options- A. 3 : 4
- B. 4 : 3
- C. 5 : 3
- D. Data inadequate Discuss
Correct Answer: 4 : 3
Explanation:
(20 x 16) women can complete the work in 1 day.
| ∴ 1 woman's 1 day's work = | 1 | . |
| 320 |
(16 x 15) men can complete the work in 1 day.
| ∴ 1 man's 1 day's work = | 1 |
| 240 |
| So, required ratio |
|
||||||
|
|||||||
| = 4 : 3 (cross multiplied) |
- 2. X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
Options- A. 6 days
- B. 10 days
- C. 15 days
- D. 20 days Discuss
Correct Answer: 10 days
Explanation:
| Work done by X in 4 days = | ❨ | 1 | x 4 | ❩ | = | 1 | . |
| 20 | 5 |
| Remaining work = | ❨ | 1 - | 1 | ❩ | = | 4 | . |
| 5 | 5 |
| (X + Y)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 8 | = | 2 | . |
| 20 | 12 | 60 | 15 |
| Now, | 2 | work is done by X and Y in 1 day. |
| 15 |
| So, | 4 | work will be done by X and Y in | ❨ | 15 | x | 4 | ❩ | = 6 days. |
| 5 | 2 | 5 |
Hence, total time taken = (6 + 4) days = 10 days.
- 3. A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
Options- A.
1 4 - B.
1 10 - C.
7 15 - D.
8 15
Discuss
Correct Answer:
| 8 |
| 15 |
Explanation:
| A's 1 day's work = | 1 | ; |
| 15 |
| B's 1 day's work = | 1 | ; |
| 20 |
| (A + B)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 7 | . |
| 15 | 20 | 60 |
| (A + B)'s 4 day's work = | ❨ | 7 | x 4 | ❩ | = | 7 | . |
| 60 | 15 |
| Therefore, Remaining work = | ❨ | 1 - | 7 | ❩ | = | 8 | . |
| 15 | 15 |
- 4. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options- A. Rs. 375
- B. Rs. 400
- C. Rs. 600
- D. Rs. 800 Discuss
Correct Answer: Rs. 400
Explanation:
| C's 1 day's work = | 1 | - | ❨ | 1 | + | 1 | ❩ | = | 1 | - | 7 | = | 1 | . |
| 3 | 6 | 8 | 3 | 24 | 24 |
| A's wages : B's wages : C's wages = | 1 | : | 1 | : | 1 | = 4 : 3 : 1. |
| 6 | 8 | 24 |
| ∴C's share (for 3 days) = Rs. | ❨ | 3 x | 1 | x 3200 | ❩ | = Rs. 400. |
| 24 |
- 5. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Options- A. 20 days
- B.
22 1 days 2 - C. 25 days
- D. 30 days Discuss
Correct Answer:
| 22 | 1 | days |
| 2 |
Explanation:
Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
| If difference of time is 60 days, B takes | ❨ | 3 | x 60 | ❩ | = 90 days. |
| 2 |
So, A takes 30 days to do the work.
| A's 1 day's work = | 1 |
| 30 |
| B's 1 day's work = | 1 |
| 90 |
| (A + B)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 4 | = | 2 |
| 30 | 90 | 90 | 45 |
| ∴ A and B together can do the work in | 45 | = 22 | 1 | days. |
| 2 | 2 |
- 6. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in :
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 12 days Discuss
Correct Answer: 8 days
Explanation:
| (A + B + C)'s 1 day's work = | 1 | ; |
| 6 |
| (A + B)'s 1 day's work = | 1 | ; |
| 8 |
| (B + C)'s 1 day's work = | 1 | . |
| 12 |
| ∴ (A + C)'s 1 day's work |
|
||||||||||||||
|
|||||||||||||||
|
|||||||||||||||
|
So, A and C together will do the work in 8 days.
- 7. A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?
Options- A. 11:30 A.M.
- B. 12 noon
- C. 12:30 P.M.
- D. 1:00 P.M. Discuss
Correct Answer: 1:00 P.M.
Explanation:
| (P + Q + R)'s 1 hour's work = | ❨ | 1 | + | 1 | + | 1 | ❩ | = | 37 | . |
| 8 | 10 | 12 | 120 |
| Work done by P, Q and R in 2 hours = | ❨ | 37 | x 2 | ❩ | = | 37 | . |
| 120 | 60 |
| Remaining work = | ❨ | 1 - | 37 | ❩ | = | 23 | . |
| 60 | 60 |
| (Q + R)'s 1 hour's work = | ❨ | 1 | + | 1 | ❩ | = | 11 | . |
| 10 | 12 | 60 |
| Now, | 11 | work is done by Q and R in 1 hour. |
| 60 |
| So, | 23 | work will be done by Q and R in | ❨ | 60 | x | 23 | ❩ | = | 23 | hours ≈ 2 hours. |
| 60 | 11 | 60 | 11 |
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
- 8. 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options- A. 3
- B. 5
- C. 7
- D. Cannot be determined
- E. None of these Discuss
Correct Answer: 7
Explanation:
| 1 woman's 1 day's work = | 1 |
| 70 |
| 1 child's 1 day's work = | 1 |
| 140 |
| (5 women + 10 children)'s day's work = | ❨ | 5 | + | 10 | ❩ | = | ❨ | 1 | + | 1 | ❩ | = | 1 |
| 70 | 140 | 14 | 14 | 7 |
∴ 5 women and 10 children will complete the work in 7 days.
- 9. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in :
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 18 days Discuss
Correct Answer: 4 days
Explanation:
Ratio of rates of working of A and B = 2 : 1.
So, ratio of times taken = 1 : 2.
| B's 1 day's work = | 1 | . |
| 12 |
| ∴ A's 1 day's work = | 1 | ; (2 times of B's work) |
| 6 |
| (A + B)'s 1 day's work = | ❨ | 1 | + | 1 | ❩ | = | 3 | = | 1 | . |
| 6 | 12 | 12 | 4 |
So, A and B together can finish the work in 4 days.
- 10. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
Options- A. 4 days
- B. 6 days
- C. 8 days
- D. 12 days Discuss
Correct Answer: 6 days
Explanation:
| Suppose A, B and C take x, | x | and | x | days respectively to finish the work. |
| 2 | 3 |
| Then, | ❨ | 1 | + | 2 | + | 3 | ❩ | = | 1 |
| x | x | x | 2 |
| ⟹ | 6 | = | 1 |
| x | 2 |
⟹ x = 12.
So, B takes (12/2) = 6 days to finish the work.
More in Aptitude:
Programming
Copyright ©CuriousTab. All rights reserved.