Question
Three workers, A, B, and C, can complete a task in 40
days, 72 days, and 45 days respectively. They start working together, but A leaves 20 days before the work is completed, and C continues working for 5 more days after A leaves. How many days does it take to complete the whole work?Solution
Let, total amount of work = 360 units (LCM of 40, 72 and 45) Efficiency of ‘A’ = 360/40 = 9 units/day Efficiency of ‘B’ = 360/72 = 5 units/day Efficiency of ‘C’ = 360/45 = 8 units/day Let, the whole work is completed in ‘x’ days So, ‘A’ worked for ‘x – 20’ days And, ‘C’ worked for x – 20 + 5 = ‘x – 15’ days So, 9(x – 20) + 8(x – 15) + 5 × x = 360 Or, 22x = 660 Or, x = 30
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