A can finish a piece of work in 15 days and B can do it in 10 days. They worked together for 2 days and then B goes away. In how many days will A finish the remaining work?

A can finish a piece of work in = 15 days
B can finish a piece of work in = 10 days
$\therefore$ A's 1 day work $=\frac{1}{15}$
B's 1 day work $=\frac{1}{10}$
(A + B)'s 1 day work $=\frac{1}{15}+\frac{1}{10}$
$=\frac{2+3}{30}=\frac{5}{30}=\frac{1}{6}$
(A + B)'s 2 days work $=\frac{1}{6}\times 2=\frac{1}{3}$
Remaining work which will be done by A alone
$=1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$
$\therefore$ A can finish 1 work in = 15 days
A can finish $\frac{2}{3}$ work in $=15\times \frac{2}{3}$ days.
$=\frac{30}{3}$ days = 10 days.