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- Question
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
- 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.
Time and Work problems
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- 1. 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 - 2. 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 - 3. 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.
- 4. 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 - 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. 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) - 7. 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.
- 8. 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 - 9. 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 - 10. 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
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