swerve wrote:Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately ?

A. 26 days
B. 27 days
C. 23 days
D. 25 days
E. 24 days

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

Say Matt alone completes the work in m day, and Peter alone completes the work in p day.

Thus, Matt's one day work = 1/m and Peter's one day work = 1/p

=> One day work of Matt and Peter = 1/m + 1/p = 1/20

12-day work of Matt and Peter = 12/20 = 3/5

Work remaining = 1 - 3/5 = 2/5

We know that Peter alone does the 2/5th of work in 10 days, thus 10/p = 2/5 => p = 25 days.

The correct answer: D

Hope this helps!

-Jay
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swerve wrote:Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately ?

A. 26 days
B. 27 days
C. 23 days
D. 25 days
E. 24 days

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

We can let m and p be the number of days it takes Matt and Peter to complete the work independently and separately. So we have Matt's rate = 1/m and Peter's rate = 1/p. We can create the equations:

20(1/m + 1/p) = 1

and

12(1/m + 1/p) + 10(1/p) = 1

Dividing the first equation by 20, we have 1/m + 1/p = 1/20. Now, substituting 1/20 for (1/m + 1/p) in the second equation, we have:

12(1/20) + 10/p = 1

3/5 + 10/p = 1

10/p = 2/5

2p = 50

p = 25

Alternate Solution:

Since the job takes 20 days to complete by both of them working together, then in 12 days, 12/20 = 3/5 of the job is completed, and 1 - 3/5 = 2/5 of the job is left to be completed by Peter alone. We are given that Peter can complete 2/5 of the job in 10 days; therefore, Peter would complete 1/1 of the job in 10/(2/5) = 25 days.

Answer: D