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- Question
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
- Correct Answer
- 18 days
Explanation2(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
Time and Work problems
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- 1. 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.
- 2. 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.
- 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 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 - 5. 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 - 6. 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.
- 7. 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 - 8. 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 - 9. 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.
- 10. 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 = 1 : 1 240 320 = 1 : 1 3 4 = 4 : 3 (cross multiplied)
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