Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?

The correct option is $\frac{15}{2}$ days.

Let us solve the problem step-by-step by determining the work done by Mohan and Sohan individually and together.

Step 1: Determine the daily work rate for each person.
Let the total work be represented as 1 unit.
Mohan can complete the total work in 10 days.
Therefore, Mohan's 1-day work = $\frac{1}{10}$
Sohan can complete the total work in 15 days.
Therefore, Sohan's 1-day work = $\frac{1}{15}$

Step 2: Find their combined 1-day work when working together.

Combined 1-day work of Mohan and Sohan = $\frac{1}{10}+\frac{1}{15}$

Taking the LCM of 10 and 15, which is 30:

Combined 1-day work = $\frac{3+2}{30}=\frac{5}{30}=\frac{1}{6}$

Step 3: Calculate the total work completed in 3 days.
They worked together for 3 days before Mohan left.
Work completed in 3 days = $3\times \frac{1}{6}=\frac{1}{2}$

Step 4: Calculate the remaining work.

Remaining work = $1-\frac{1}{2}=\frac{1}{2}$

Step 5: Find the time taken by Sohan to finish the remaining work.
Sohan completes 1 unit of work in 15 days.
To complete the remaining $\frac{1}{2}$ unit of work, Sohan will take:

Time required = $\frac{1}{2}\times 15=\frac{15}{2}$ days

Thus, Sohan will take $\frac{15}{2}$ days to finish the remaining work.