Question:
Rajan can do a piece of work in 24 days while Amit can do it in 30 days. In how many days can they complete it, if they work together?
Solution:
Work done by Rajan in 1 day $=\frac{1}{24}$
Work done by Amit in 1 day $=\frac{1}{30}$
Work done by Amit and Rajan together in 1 day $=\frac{1}{24}+\frac{1}{30}=\frac{54}{720}=\frac{3}{40}$
$\therefore$ They can complete the work in $\frac{40}{3}$ days, i.e., $13 \frac{1}{3}$ days if they work together.