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). \(4\frac{4}{5}\) days
2). \(9\frac{2}{5}\) days
3). \(4\frac{3}{5}\) days
4). 9.5 days
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