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    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?
    A 32 Correct Answer Incorrect Answer
    B 30 Correct Answer Incorrect Answer
    C 36 Correct Answer Incorrect Answer
    D 40 Correct Answer Incorrect Answer

    Solution

    Let, total amount of work = 360 units (LCM of 40, 72 and 45) Efficiency of β€˜A’ = 360/40 = 9 units/day Efficiency of β€˜B’ = 360/72 = 5 units/day Efficiency of β€˜C’ = 360/45 = 8 units/day Let, the whole work is completed in β€˜x’ days So, β€˜A’ worked for β€˜x – 20’ days And, β€˜C’ worked for x – 20 + 5 = β€˜x – 15’ days So, 9(x – 20) + 8(x – 15) + 5 Γ— x = 360 Or, 22x = 660 Or, x = 30

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