Question
A alone can do a work in 30 days. B alone can do the
same work in 40 days. If they work on alternate days starting with A. then in how many days (correct up to two places of decimal) the work will be completed?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
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