Time and Work problems
- 1. A, B and C contract a work for Rs. 550. Together A and B are supposed to do 7/11 of the work. The share of C should be?
Options- A. Rs. 1831/3
- B. Rs. 200
- C. Rs. 300
- D. Rs. 400 Discuss
Correct Answer: Rs. 200
Explanation:
Work to be done by C = (1 - 7/11) = 4/11
? (A + B) : C = 7/11 : 4/11 = 7 : 4
? C's share = Rs. 550 x (4/11) = Rs. 200
- 2. A and B separately can complete a work in 6 days and 3 days respectively. If they work together, then in how many days will they complete the work?
Options- A. 4 days
- B. 3 days
- C. 2 days
- D. 5 days Discuss
Correct Answer: 2 days
Explanation:
Work completed by A + B in one day = 1/6 + 1/3 = 1/2
? Time taken by A + B to complete the work = 2 days.
- 3. Ram, Dilip and Shekhar can complete a work in 20 days. If Ram and Dilip together can complete the same work in 30 days, then how long will Shekhar take to complete it?
Options- A. 60 days
- B. 62 days
- C. 40 days
- D. 56 days Discuss
Correct Answer: 60 days
Explanation:
? Work of (Ram + Dilip + Shekhar) for 1 day = 1/20
and work of (Ram + Dilip) for 1 day = 1/30
? Work of Shekhar for 1 day = 1 / 20 - 1 / 30 = 1/60
Hence, Shekhar will complete the work in 60 days.
- 4. Sunil complete a work in 4 days whereas Dinesh completes the work in 6 days. Ramesh work 1 1/ 2 times as fast as sunil. How many days it will take for the three together to complete the work?
Options- A. 7 / 12
- B. 15/12
- C. 15/7
- D. None of these Discuss
Correct Answer: None of these
Explanation:
Time taken by Ramesh alone = (2/3) x 4 = 8/3 days
? Their 1 day's work = (1/4 + 1/6 + 3/8) = 19/24
So, together they can finish the work in 24 /19 days, i.e., 15/19 days.
- 5. Mahesh and Umesh can complete a work in 10 days and 15 days respectively. Umesh starts the work and after 5 days Mahesh also joins him. In all the work would be completed in?
Options- A. 7 days
- B. 9 days
- C. 11 days
- D. None of these Discuss
Correct Answer: 9 days
Explanation:
Umesh's 5 day's work = 5 x (1/15) = 1/3
Remaining work = (1 - 1/3) = 2/3
(1/10 + 1/15) work is done by both in 1 day
? 2/3 work is done by both in 6 x (2/3) = 4 days
Hence, the work was completed in 4 + 5 = 9 days.
- 6. A can do a piece of work in 80 days. He works at it For 10 days and then B alone finishes the work in 42 days. The two together could complete the work in?
Options- A. 24 days
- B. 25 days
- C. 30 days
- D. 35 days Discuss
Correct Answer: 30 days
Explanation:
A's 10 day's work = (10 x 1/80) = 1/8
Remaining work = (1 - 1/8) = 7/8
? 7/8 work is done by B in 42 days
? Whole work will be done by B in (42 x 8/7) = i .e., 48 days.
? (A + B)'s day's work = (1/80 + 1/48) = 8/240 = 1/30
Hence, A and B together can finish it in 30 days.
- 7. A can do a certain job in 25 days which B alone can do in 20 days. A started the work and was joined by B after 10 days. The work lasted for?
Options- A. 121/2
- B. 142/9
- C. 15 days
- D. 162/3 Discuss
Correct Answer: 162/3
Explanation:
A's 10 day's work = 10 x (1/25) = 2/5
Remaining work = 1 - 2/5 = 3/5
Work was done by (A + B) in 1 day = (1/25 + 1/20) = 9/100
? 3/5 work was done by (A + B) in (100/9 x 3/5) = 20/3 days
Hence, the work lasted for (10 + 62/3) = 162/3 days.
- 8. 14 men can complete a work in 12 days. 4 days after they started the work, 2 more men joined them. How many days will they take to complete the remaining work?
Options- A. 9 days
- B. 5 days
- C. 6 days
- D. 7 days Discuss
Correct Answer: 7 days
Explanation:
? In 12 days work done by 14 men = 1
? In 4 days work done by 14 men = 1 x 4/12 = 1/3
? Remaining work = 1 - 1/3 = 2/3
and number of total men = 14 + 2 = 16
If 1 work is done by 14 men in 12 days
? 2/3 work is done by 16 men in 12 x (14/16) x (2/3) = 7 days
- 9. 12 men can complete a work within 9 days. After 3 days they started the work, 6 men joined them to replace 2 men. How many days will they take to complete the remaining work?
Options- A. 2
- B. 3
- C. 4
- D. 41/2 Discuss
Correct Answer: 41/2
Explanation:
12 men can complete 1/3 of the work in 3 days and the remaining 2/3 of the work in 6 days.
1 man can complete 2/3 of the work in (12 x 6) = 72 days
? (12 - 2 + 6) = 16 men can complete 2/3 of thye work in 72/16 = 41/2 days
- 10. you can do a piece of work in 8 days, B can do it in 16,While C can do it in 80 days. In how many days they can complete the whole work, working together?
Options- A. 5
- B. 6
- C. 8 2/3
- D. 20 2/5 Discuss
Correct Answer: 5
Explanation:
Efficiency of A = 12.5%
Efficiency of B = 6.25%
Efficiency of C = 1.25%
Efficiency of (A+ B + C) = (12.5 +6.25 + 1.25) = 20%
Required no of days = 100/20 = 5 days
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