A alone can do a work in 30 days. B alone can do the

Solution

A can do a work in 30 days B can do a work in 40 days Total work done by A & B both = LCM of 30 & 40 = 120  Efficiency of A = 120/30 = 4  Efficiency of B = 120/40 = 3 Work done by A on 1st day = 120/30 = 4 Work done by B on 2nd day = 120/40 = 3 Work done in first 2 days by A & B = 4  + 3 = 7 then, work done in (2 x 17 = 34) days by A & B = 17 x 7 = 119   ⇒ Remaining work will be done by A = (120 – 119)/4 = 1/4 day ⇒ Total time = 34 + 1/4 = 34(1/4) days ∴ The work will be done in 34(1/4) days