X can do a piece of work in 25 days and Y can finish it in 20 days. They work together for 5 days and then X leaves. In [[1]] days will Y finish the remaining work.

Find the job that X and Y completed in one day. therefore they discover their task completed in 5 days. Subtract the work completed by $(X + Y)$ in 5 days from one to obtain the work that has to be completed by Y. Therefore, determine how many days it will take Y to complete the task.

Step -1: figuring out how much X and Y work each day.
Let there be one work in whole.
Then, based on question X, it takes 25 days to do one task.
Then X completed the assignment in one day $=\frac{1}{25}$.
In accordance with question Y, it takes 20 days to complete one task. Then Y completed the task in one day$=\frac{1}{20}$.
Together, they completed the job in one day. $=\frac{1}{20}+\frac{1}{25}=\frac{9}{100}$
Step -2: calculating the number of days needed.
Together, they put in a lot of labour. 5 days $=5\times \frac{9}{100}=\frac{45}{100}$
Then all job was done $=1-\frac{45}{100}=\frac{55}{100}$
Now that Y can complete 1 task in 20 days,
Y can do $\frac{55}{100}$ work in $\frac{55}{100}\times 20$ days $=11$ days

Hence, the correct answer is option 11 days.