A can finish a piece of work in 25 days and B can finish it in 20 days. They work together for 5 days and then A leaves. In how many days will B finish the remaining work?

Correct option is C

Given:
- A can finish the work in 25 days.
- B can finish the work in 20 days.
- They work together for 5 days, then A leaves.
Concept Used:

Work done in 1 day: If a person can complete work in D days, then the work done per day by that person is  $$\frac{1}{D}$$​​
-Work done by two people in one day:If two people A and B have individual work rates $$\frac{1}{D_A}$$​ and $$\frac{1}{D_B}$$​, their combined work per day is $$\frac{1}{D_A} + \frac{1}{D_B}$$​​
-Remaining Work:If part of the work is completed, the remaining work can be found by subtracting the completed work from the total work.
Solution:

- Work rate of A = $$\frac{1}{25}$$​​
- Work rate of B = $$\frac{1}{20}$$​​
Calculate the combined work rate of A and B:
Combined work rate =  $$\frac{1}{25} + \frac{1}{20} = \frac{4 + 5}{100} = \frac{9}{100}$$​​
The work done by A and B in 5 days:
Work done in 5 days =$$5 \times \frac{9}{100} = \frac{45}{100} = 0.45$$​​
Remaining work:
Remaining work = 1 - 0.45 = 0.55

The number of days B will take to finish the remaining work:
Days required by B = $$\frac{\text{Remaining work}}{\text{B's work rate}} = \frac{0.55}{\frac{1}{20}} = 0.55 \times 20 = 11 \text{ days}$$​​
B will finish the remaining work in 11 days.