A, B and C can complete a task in 32, 16 and 24 days respectively. They start working together but A leaves 4 days after the start of the work while B leaves 6 days before the works gets completed. Find B's share out of Rs. 3120?
Explanation:
Let the work to be done = LCM (32, 16, 24) = 96 units
∴ Efficiency of A = 96/32 = 3 units/day Efficiency of B = 96/16 = 6 units/day Efficiency of C = 96/24 = 4 units/day
Let the time taken to complete the entire work = x days.
A works for 4 days. B works for (x - 6) days C works for x days
Total work done = Work done by A in 4 days + Work done by B in (x - 6) days + Work done by C in x days.
⇒ 96 = 3 × 4 + 6 × (x - 6) + 4 × x ⇒ 96 = 12 + 6x - 36 + 4x ⇒ 120 = 10x ⇒ x = 12
∴ B worked for 12 - 6 = 6 days ⇒ Work done by B = 6 × 6 = 36 units
⇒ Fraction of work done by B = 3696 = 38 units
⇒ Payment for B = 38 × 3120 = 1170
Hence, option (a).
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