A and B can do a piece of work in 21 and 24 days respectively. They start the work together and after some days A leaves the work and B completes the remaining work in 9 days. After how many days did A leave?

Let the total work be LCM of (21, 24) = 168 units.

Amount of work done by A on 1 day = $$\ \frac{\ 168}{21}$$ = 8 units

Amount of work done by B on 1 day = $$\ \frac{\ 168}{24}$$ = 7 units

Let p be the number of days for which they worked together.

In P days, the amount of work done by A and B = 15p

Remaining work = 168x-15p, which is completed by B in 9 days.

168x-15p=9*7

p=7

So A left after 7 days.

B is the correct answer.