A does $60\%$ of a work in 15 days. He then calls B, and they together finish the remaining work in 5 days. How long B alone would take to do the whole work?

A completes $60\%$ ($\frac{3}{5}$) of the work in 15 days.Time taken by A to complete the whole work:
$$\text{Total time for A}=15\times \frac{5}{3}=25\text{ days}$$
So, A's 1-day work rate = $\frac{1}{25}$.The remaining work is $100\%-60\%=40\%$ ($\frac{2}{5}$).A and B together finish this remaining $\frac{2}{5}$ of the work in 5 days.Time taken by A and B together to complete the whole work:
$$\text{Total time for A + B}=5\times \frac{5}{2}=12.5\text{ days}=\frac{25}{2}\text{ days}$$
So, (A + B)'s 1-day work rate = $\frac{2}{25}$.Now, B's 1-day work rate can be found by subtracting A's rate from the combined rate:
$$\text{B’s 1-day work}=\frac{2}{25}-\frac{1}{25}=\frac{1}{25}$$
Therefore, B alone will take 25 days to complete the whole work.