A can do a work alone in 10 days. B can do the same work alone in 15 days. They start together but B leaves the job 2 days after start and A completes the remaining work alone. What is the total number of days in which the work is completed?

Let's assume the total work is 30 units.

A can do a work alone in 10 days.

Efficiency of A = $$\frac{30}{10}$$ = 3 units/day

B can do the same work alone in 15 days.

Efficiency of B = $$\frac{30}{15}$$ = 2 units/day

They start together but B leaves the job 2 days after start and A completes the remaining work alone.

Let's assume the number of days A work alone is 'y'.

$$(3+2)\times2 + 3y = 30$$

$$5\times2 + 3y = 30$$

10 + 3y = 30

3y = 30-10 = 20

$$y=\frac{20}{3}$$

The total number of days in which the work is completed = $$2+y$$

= $$2+\frac{20}{3}$$

= $$\frac{6}{3}+\frac{20}{3}$$

= $$\frac{26}{3}$$ days