Time and Work problems
- 1. 12 men and 16 boys can do a piece of work in 5 days while 13 men and 24 boys finish it in 4 days. 5 men and 10 boys will finish it in?
Options- A. 10 days
- B. 12 days
- C. 9 days
- D. 15 days Discuss
Correct Answer: 10 days
Explanation:
(12 men + 16 boys) can do a work in 5 days.
(60 men + 80 boys) can do a work in 1 day.
(13 men + 24 boys) can do a work in 4 days.
(52 men + 96 boys) can do a work in 1 day.
? 60 men + 80 boys = 52 men + 96 boys
8 men = 16 boys and 1 man = 2 boys
Now, 12 men + 16 boys = (12 x 2 + 16) boys
= 40 boys can do the work in 5 days
? 5 men + 10 boys = [5 x 2 + 10] boys
= 20 boys will take
= (40 x 5)/20 = 10 days
- 2. 'A' can do a piece of work in 2 hours, 'B' can do thrice the work in 8 hours and 'C' can do the same work as 'A' in 8 hours. If all of them work together, how long it would take them to complete the work?
Options- A. 1 hour
- B. 2 hour
- C. 3 hour
- D. 4 hours Discuss
Correct Answer: 1 hour
Explanation:
Efficiency of A = 50% [100/2]
Efficiency of B = 37.5% [100/(8/3)]
Efficiency of C = 12.5% [100/8]
Combined efficiency of A,B and C = 100%
So, they complete the work in 1 hour.
- 3. If one man or two woman or three boys can finish a work in 88 days , then how many days will one man one woman and one boys together take to finish the same work?
Options- A. 46 boys
- B. 54 days
- C. 48 days
- D. 44 days Discuss
Correct Answer: 48 days
Explanation:
1 man = 2 woman = 3 boys
? 1 man + 1 woman + 1 boy = (3 + 3/2 + 1) boys = 11/2 boys
Here M1 = 3 M2 = 11/2, D1 = 88 and D2 = ?
According to the formula
M1D1 = M2D2
? D2 = M1D1/M2
? Required number of days
= 3 x 2 x 88/11 = 3 x 2 x 8 = 48 days
- 4. When A alone does a piece of work, he takes 25 days more than the time taken by (A + B) to complete that particular work, while B alone takes 49 days more than the time taken by (A + B) to finish the same work . A and B together will take what time for finish this work?
Options- A. 35 days
- B. 25 days
- C. 15 days
- D. 45 days Discuss
Correct Answer: 35 days
Explanation:
According to the formula,
Required time = ?ab
Where a = 25 and b = 49
? Require time = ?25 x 49 = 5 x 7
= 35 days
- 5. X can do 1/4 of work in 10 days, Y can do 40% of the same work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first?
Options- A. X
- B. Y
- C. Z
- D. Both X and Z Discuss
Correct Answer: Z
Explanation:
Time taken to complete the work by X =10 x 4 = 40 = 40 days
Time taken to complete the work by Y = (40 x 100)/40 = 100 days
Time taken to complete the work by Z = 13 x 3 = 39 days
Hence, Z will complete the work first.
- 6. P and Q can finish a work in 30 days, They work at it for 10 days and then Q left. The remaining work is done by P alone in 20 more days. How long will P take to finish the work alone?
Options- A. 30 days
- B. 20 days
- C. 60 days
- D. 50 days Discuss
Correct Answer: 30 days
Explanation:
(P + Q)'s 10 day's work= (1/30) x 10 = 1/3
Remaining work = (1 -1/3) = 2/3
2/3 work is done by P in 20 days.
? Whole work is done by P in 20 x (3/2) = 30 days
- 7. A and B can do a piece of work in 60 days and 75 days, respectively. Both begin together but after a certain time A leaves off. In such case B finishes the remaining work in 30 days. After how many days did A leave?
Options- A. 25 days
- B. 21 days
- C. 20 days
- D. 24 days Discuss
Correct Answer: 20 days
Explanation:
Here A = 60 days, B = 75 days, D = 30, T = ?
? Required time = (B - D) x [A/(A + B)]
= (75 - 30) x [60/(60 + 75)]
= (45 x 60)/135 = 20 days
? Required time = 20 days
- 8. 20 women can complete apiece of work in 7 day. If 8 more women are put on the job. In how many days will they complete the work?
Options- A. 4.5 days
- B. 5 days
- C. 5.5 days
- D. 4.5 days Discuss
Correct Answer: 5 days
Explanation:
Given, M1 = 20 D1 = 7, M2 = 20 + 8 = 28
and D2 = ?
Using formula, M1D1 = M2D2
? 20 x 7 = 28 x D2
? D2 = (20 x 7)/28 = 5 days
- 9. 12 men can do a piece of work in 24 days. How many days are needed to go complete the work, if 8 men do this work?
Options- A. 28
- B. 36
- C. 48
- D. 52 Discuss
Correct Answer: 36
Explanation:
Given, M1 = 12, M2 = 8 , D1 = 24 , W1 = 1, W2 = 1
According to the formula,
M1D1W2 = M2D2W1
? 12 x 24 x 1= 8 x D2 x 1
? D2 = (12 x 24)/8
= 12 x 3 = 36 days
- 10. 20 men can cut 30 tree in 4 h. If 4 men leave the job, how many trees will be cut in 12 h?
Options- A. 72
- B. 80
- C. 68
- D. 79 Discuss
Correct Answer: 72
Explanation:
Given, M1 = 20, T1 = 4, W1 = 30,
M2 = 20 - 4 = 16, T2 = 12 and W2 = ?
According to the formula,
M1T1W2 = M2T2W1
? 20 x 4 x W2 = 16 x 12 x 30
? W2 = (16 x 12 x 30)/(20 x 4) = 12 x 6 = 72 trees
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