A and B together are finish a piece of work in 15 days. A lone can finish it in 24 days. In how many days can B alone do it?

A and B complete a work in 15 days 

one day work of $(A+B)=\frac{1}{15}$

A can finish the work in $=24$ days

one day’s work of $A=\frac{1}{24}$

Then B alone finish the work $=\frac{1}{15}-\frac{1}{24}$

$=\frac{8-5}{120}=\frac{3}{120}=\frac{1}{40}$

B can complete the work in 40 days