A alone can complete a task in 27 days while B alone can complete the same task in 45 days. Both of them started the work together, but A left 5 days before actual completion of work. Find how many days did a work?
Explanation:
Let the work to be done = LCM (27, 45) = 135 units.
∴ Efficiency of A = 135/27 = 5 units/day, and Efficiency of B = 135/45 = 3 units/day
Let A and B together work for 'x' days after which B completes the remaining work in 5 days.
∴ Total work done = Work done by A and B in x days + Work done by B in last 5 days.
⇒ 135 = (5 + 3) × x + 3 × 5 ⇒ 135 = 8x + 15 ⇒ 120 = 8x ⇒ x = 120/8 = 15 days.
∴ A and B together worked for 15 days.
Hence, option (b).
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