Time and Work problems
- 1. A, Band C can do a piece of work individually in 8, 12 and 15 days, respectively. A and B start working but A quits after working for 2 days. After this, C joins B till the completion of work. In how many days will the work be completed?
Options- A. 58/9 days
- B. 46/7 days
- C. 67/13 days
- D. 33/4 days Discuss
Correct Answer: 58/9 days
Explanation:
Work done by A and B in 1 day
= (1/8) + (1/12) = 5/24
2 day's work of A and B = 10/24
After 2 day's A left the work
? Remaining work = 1 - (10/24) = 14/24
One day work of B and C together = (1/12) + (1/15) = 9/60
So, the number of days required by B and C to finish work
= (14/24) / (9/60) = (14/24) x (60/9) = 35/9
? Total days to complete the work = 2 + (35/9) = 53/9 = 58/9 days
- 2. A and B can do a piece of work in 9 days and 18 days, respectively. As they were ill, they could do 90% and 72% of their efficiency, respectively. How many days will they take to complete the work together?
Options- A. 71/7
- B. 8
- C. 5
- D. 121/2 Discuss
Correct Answer: 71/7
Explanation:
Because of illness,
A's 1 day's work = 90% of 1/9 = 1/10
B's 1 day's work = 72% of 1/18 = 1/25
? (A + B)'s 1 day's work
= (1/10) + (1/25) = (5 + 2)/50 = 7/50
Hence, time taken by them to complete the work = 50/7 days
= 71/7
- 3. 36 workmen are employed to finish a certain work in 48 days. But it is found that in 24 days only 2/5 work is done. How many more men must be employed to finish the work in this?
Options- A. 16
- B. 18
- C. 20
- D. 22 Also asked in: Bank Exams, Bank PO
Correct Answer: 18
Explanation:
Let N men are employed.
Given, M1 = 36, M2 = 36 + N, D1 = 24,
D2 = 24, W1 = 2/5, W2 = 1 - 2/5 = 3/5
According to the formula M1D1W2 = M2D2W1
? 36 x 24 x (3/5) = (36 + N) x 24 x (2/5)
? 36 x 3 = 2(36 + N) ? 108 = 72 + 2N
? N = 36/2 = 18 men
- 4. It is given that 16 men working 18 h a day can build a wall 36 m long, 4 m broad and 24 m high in 20 days. How many men will be required to build a wall 64 m long, 6 m broad and 18 m high working 12 h a day in 16 days?
Options- A. 60
- B. 20
- C. 30
- D. 35 Discuss
Correct Answer: 60
Explanation:
Given, M1 = 16, T1 = 18,
W1 = 36 x 4 x 24, D1 = 20 and M2 = ?
T2 = 12, W2 = 64 x 6 x 18, D2 = 16
According to the formula,
M1D1T1/ W1 = M2D2T2/ W2
? 16 x 20 x (18/36) x 4 x 24 = M2 x 12 x (16/64) x 6 x 18
? (15/36) x 24 = M2 x (2/64) x 6 x 18
? M2 = 60 men
- 5. A men can do a piece of work in 5 days. With the help of his friend, he can do the same work in 3 days. In how many days can his friend complete the work?
Options- A. 6 days
- B. 61/2 days
- C. 7 days
- D. 71/2 Discuss
Correct Answer: 71/2
Explanation:
(Man and his friend)'s 1 day's work = 1/3
Men's 1 day's work = 1/5
His friend's 1 day's work is = 1/3 - 1/5 = 2/15
Hence, his friend can complete the work in 15/2 = 71/2
- 6. A and B each working alone can do a work in 15 days and 25 days, respectively. They started the work together but B left after some time and A finished the remaining work in 7 days. After how many days from the start did B leave?
Options- A. 3
- B. 5
- C. 7
- D. 9 Discuss
Correct Answer: 5
Explanation:
Let B left work after N days from the start.
According to the question,
N/25 + (N + 7)/15 = 1
? (3N + 5N + 35) / 75 = 1
? 8N = 75 - 35
? N = 40/8
? N = 5
- 7. A can complete a work in 20 days and B in 30 days. A worked alone for 4 days and then B complete the remaining work alone with C in 18 days. In how many days can C working alone complete the work?
Options- A. 12
- B. 68
- C. 72
- D. 90 Discuss
Correct Answer: 90
Explanation:
Work done by A in 4 days = 4/20 = 1/5
? Remaining work = 1 - 1/5 = 4/5
Let C can working alone complete the work in N days .
According to the question,
18/30 + 18/N = 4/5
? 18(N + 30) x 5 = 4 x 30 x N
? 90N + 2700 = 120N
? 30N = 2700
? N = 90 days
- 8. 6 men can do a piece of work in 12 days while 8 women can do the same work in 18 days. The same work can be done by 18 children in 10 days. 4 men 12 women and 20 children work together for 2 days. If only men have to complete remaining work in 1 day, then find the required number of men.
Options- A. 36
- B. 24
- C. 18
- D. couldn't be determind Discuss
Correct Answer: 36
Explanation:
6 x 12 men = 8 x 18 women = 18 x 10 children
? 12 men = 24 women = 30 children
? 2 men = 4 women = 5 children
Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men
Time to do remaining work in 1 man = (6 x 12 - 18 x 2) = 36 days
? Required number of men to finish the work in 1 days = 36
- 9. A, B and C can do a piece of work in 18, 24 and 36 days, respectively. They work alternately, first day C, second day B and third day A, fourth day C and so on. How many days will be needed to complete the work like this way?
Options- A. 18
- B. 20
- C. 24
- D. 30 Discuss
Correct Answer: 24
Explanation:
Work done in first in 3 days
= (1/18) + (1/24) + (1/36) = (4 + 3 + 2)/72 = 1/8
? Time taken to complete 1/8 part of work = 3 days
? Time taken to complete the whole work = 3 x 8 = 24 days
- 10. 16 children and 24 men complete a certain work for 18 days. If each child takes twice the time taken by a man to finish the work in how many days will 24 men finish the same work?
Options- A. 12 days
- B. 24 days
- C. 36 days
- D. 48 dyas Discuss
Correct Answer: 24 days
Explanation:
According to the question,
2 children = 1 man
? (16 children + 24 men) = (8 + 24) men = 32 men
Given M1 = 32, M2 = 24, D1 = 18, D2 = ?
and W1 = W2 = 1
According to the formula, M1D1W2 = M2D2W1
? 32 x 18 x 1 = 24 x D2 x 1
? D2 = (32 x 18)/24 = 8 x 3 = 24 days
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