A can finish a piece of work in = 15 days
B can finish a piece of work in = 10 days
∴ A’s 1 day work = 1/15
B’s 1 day work = 1/10
(A + B)’s 1 day work = 1/15 + 1/10
= (2 + 3)/30 = 5/30 = 1/6
(A + B)’s 2 day work = (1/6) × 2 = 1/3
Remaining work which will be done by A alone
= 1 – (1/3) = (3 – 1)/3 = 2/3
∴ A can finish 1 work in = 15 days
A can finish 2/3 work in = 15 × (2/3) days
= 30/3 days = 10 days