Time and Work problems
- 1. A can do a piece of work in 12 days. B is 60% more efficient than A. The number of days, it take B to do the same piece of work is?
Options- A. 71/2
- B. 61/4
- C. 8
- D. 6 Discuss
Correct Answer: 71/2
Explanation:
A's 1 day's work = 1/12
B's 1 day's work = 1/12 + 60% of 1/12 = 1/12 x 160/100 = 2/15
? B can do the work in 15/2 days = 71/2 days.
- 2. A can finish a piece of work in 12 days while B can do it in 15 days. If both work at it together, what time will they take to do the work?
Options- A. 6 days
- B. 8 days
- C. 62/3 days
- D. 101/15 days Discuss
Correct Answer: 62/3 days
Explanation:
Efficiency of A = 100/12 = 8.33%
Efficiency of B = 100/15 = 6.66%
Combined efficiency of A and B = 8.33 + 6.66 = 15%
Number of days taken by A and B, when worked together = 100/15
= 62/3 days
- 3. A can do a piece of work in 14 days while B can do it in 21 days. In how many days, working together they will complete the whole work?
Options- A. 10.5
- B. 8
- C. 8.4
- D. 9 Discuss
Correct Answer: 8.4
Explanation:
One day's work of A and B = 1/14 + 1/21 = 5/42
? Required number of days = 42/5 = 8.4 days
- 4. A can do a piece of work in 24 days. If B is 60% more efficient than A, then the number of days required by B to do the same piece of work is?
Options- A. 10
- B. 15
- C. 12
- D. 9.6 Discuss
Correct Answer: 15
Explanation:
Efficiency of A = 4.16%
Efficiency of B = 1.6 x 4.16 = 6.66%
? Number of days required by B = 100/6.66 = 15 days
- 5. A is twice as good a workman as B and together they finish a piece of work in 14 days. In how many days can a alone finish the work?
Options- A. 18
- B. 20
- C. 21
- D. 24 Discuss
Correct Answer: 21
Explanation:
One day's work of A and B = 1/x + 1/2x = 1/14
? x = 21
Since A is twice efficient as B so A will take half of the day taken by B.
- 6. Ajit is 3 times as efficient as Bablu, then the ratio of number of days required by each to work alone, completely?
Options- A. 3 : 1
- B. 1 : 3
- C. 6 : 3
- D. 3 : 6 Discuss
Correct Answer: 1 : 3
Explanation:
Efficiency of Ajit : Bablu = 3 : 1
No. of days 1 : 3
- 7. X is 4 times more efficient as Y , then the number of days taken by X and Y are in the ratio?
Options- A. 8 : 1
- B. 1 : 5
- C. 6 : 8
- D. 5 : 1 Discuss
Correct Answer: 1 : 5
Explanation:
Efficiency (X : Y) = 5 : 1
No. of days (X : Y) = 1 : 5
- 8. Sonu can do a piece of work in 20 days. He started the work and left after some days, when 25% work was done. After it Abhijeet joined and completed it working for 10 days. In how many days Sonu and Abhijeet can do the complete work, working together?
Options- A. 6
- B. 8
- C. 10
- D. 12 Discuss
Correct Answer: 8
Explanation:
Efficiency of Sonu = (100/20) = 5%
Rest work = 75%
? Efficiency of Abhijeet = 75/10 = 7.5%
? Combined efficiency of Sonu and Abhijeet = 7.5 + 5 = 12.5%
? Number of days required by Sonu and Abhijeet, to work togethere = 100/12.5 = 8days
- 9. Three taps A, B and C together can fill a tank in 6 h. After working 2 h, C is closed and the tank was filled in 8 h more. Find the time in which C alone can fill the tank?
Options- A. 12 h
- B. 16 h
- C. 14 h
- D. 18 h Discuss
Correct Answer: 12 h
Explanation:
Work of (A + B + C) in 1 H = 1 / 6
Work done in 2 h = 2/6 = 1/3
Remaining part of the tank = 1 - 1/3 = 2/3
Time taken by A + B to fill this 2/3rd part of the tank = 8 h
A and B together can fill tank in 12 h (i.e., 8 x 3/2).
Now, we have A, B and C together filling the tank in 6 h and A and B together fill tank in 12 h.
Work done by C alone in 1 h = 1/6 - 1/12 = 1/12
Hence, C alone can fill the tank in 12 h.
- 10. Alen and Border can do a work individually in 21 and 42 days respectively. In how many days they can complete the work, working alternatively?
Options- A. 14
- B. 28
- C. 42
- D. 35 Discuss
Correct Answer: 28
Explanation:
Alen's one day's work =1/21
Border's one day's work = 1/42
Alen and Border's two days work(working alternatively) = (1/21) + (1/42) = 1/14
So, Alen and Border do 1/14 work in 2 days
So, they complete the work in 14 x 2 = 28 days.
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