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A and B can separately do a piece of work in 8 and 12 days respectively. How much time will it take to finish the whole work if they work alternatively starting by A?1). \(4\frac{4}{5}\) days2). \(9\frac{2}{5}\) days3). \(4\frac{3}{5}\) days4). 9.5 days |
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Answer» Time taken by A = 8 days Time taken by B = 12 days Let Total work = LCM of 8 and 12 = 24 units ⇒ Efficiency of A = 24/8 = 3 units/day ⇒ Efficiency of B = 24/12 = 2 units/day ⇒ Efficiency of A and B together = 3 + 2 = 5 units/2 days By working alternatively,they would COMPLETE 20 units of work in 8 days. Remaining work = 24-20 = 4 units of these 4 units of work,first 3 units would be completed by A(as he STARTED the work) and 1 unit by B. time taken = 1+1/2 = 1.5 days ∴ Total time taken to complete the work = 9.5 days |
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