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- Question
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Options- A. 4 days
- B. 5 days
- C. 6 days
- D. 7 days
- Correct Answer
- 4 days
ExplanationLet 1 man's 1 day's work = x and 1 boy's 1 day's work = y.Then, 6x + 8y = 1 and 26x + 48y = 1 . 10 2 Solving these two equations, we get : x = 1 and y = 1 . 100 200 (15 men + 20 boy)'s 1 day's work = ❨ 15 + 20 ❩ = 1 . 100 200 4 ∴ 15 men and 20 boys can do the work in 4 days.
Time and Work problems
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- 1. 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.
- 2. 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.
- 3. 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.
- 4. 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.
- 5. 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.
- 6. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Options- A. 15
- B. 16
- C. 18
- D. 25 Discuss
Correct Answer: 16
Explanation:
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4.Suppose Tanya takes x days to do the work.
5 : 4 :: 20 : x ⟹ x = ❨ 4 x 20 ❩ 5 ⟹ x = 16 days.
Hence, Tanya takes 16 days to complete the work.
- 7. A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Options- A. 5
- B.
5 1 2 - C. 6
- D. 8 Discuss
Correct Answer: 6
Explanation:
B's 10 day's work = ❨ 1 x 10 ❩ = 2 . 15 3 Remaining work = ❨ 1 - 2 ❩ = 1 . 3 3 Now, 1 work is done by A in 1 day. 18 ∴ 1 work is done by A in ❨ 18 x 1 ❩ = 6 days. 3 3 - 8. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
Options- A. 30 days
- B. 40 days
- C. 60 days
- D. 70 days Discuss
Correct Answer: 60 days
Explanation:
Let A's 1 day's work = x and B's 1 day's work = y.Then, x + y = 1 and 16x + 44y = 1. 30 Solving these two equations, we get: x = 1 and y = 1 60 60 ∴ B's 1 day's work = 1 . 60 Hence, B alone shall finish the whole work in 60 days.
- 9. A, B and C can complete a piece of work in 24, 6 and 12 days respectively. Working together, they will complete the same work in:
Options- A.
1 day 24 - B.
7 day 24 - C.
3 3 days 7 - D. 4 days Discuss
Correct Answer:3 3 days 7
Explanation:
Formula: If A can do a piece of work in n days, then A's 1 day's work = 1 . n (A + B + C)'s 1 day's work = ❨ 1 + 1 + 1 ❩ = 7 . 24 6 12 24 Formula: If A's 1 day's work = 1 , then A can finish the work in n days. n So, all the three together will complete the job in ❨ 24 ❩ days = 3 3 days. 7 7 - 10. A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:
Options- A. 5 days
- B. 6 days
- C. 10 days
- D.
10 1 days 2
Discuss
Correct Answer: 10 days
Explanation:
(B + C)'s 1 day's work = ❨ 1 + 1 ❩ = 7 . 9 12 36 Work done by B and C in 3 days = ❨ 7 x 3 ❩ = 7 . 36 12 Remaining work = ❨ 1 - 7 ❩ = 5 . 12 12 Now, 1 work is done by A in 1 day. 24 So, 5 work is done by A in ❨ 24 x 5 ❩ = 10 days. 12 12
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