A and B working separately can do a piece of work in 9 and 15 days respectively. If y work for a day alternately, with A beginning, n work will be completed in:

Work rate of A = $$\frac{{100}}{9}$$ = 11.11% work per day
Work rate of B = $$\frac{{100}}{{15}}$$ = 6.66% work per day

They together can do (A + B) = 11.11 + 6.66 ≈ 18% work per day
They are working in alternate day, so we take 2 days = 1 unit of day
Therefore, in one unit of day they can complete 18% of work
(A + B) can complete 90% of work in 5 units of days. i.e. (5 × 18)
And the rest 10% work will be completed by A in Next day
So, total number of day,
= 5 Unit of days + 1 day of A
= 2 × 5 + 1 = 11 days