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- Question
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
- Correct Answer
- Rs. 400
ExplanationC'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
Time and Work problems
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- 1. 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 - 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. 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) - 4. 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.
- 5. 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 - 6. 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 - 7. 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 = ❨ 2 x 1 ❩ - ❨ 1 + 1 ❩ 6 8 12 = ❨ 1 - 5 ❩ 3 24 = 3 24 = 1 . 8 So, A and C together will do the work in 8 days.
- 8. 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.
- 9. 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.
- 10. 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.
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