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    Question

    β€˜P’, β€˜Q’, and β€˜R’ can

    complete a task in 10 days, 15 days, and 20 days, respectively. β€˜P’ starts the task alone and is joined by β€˜Q’ on the second day. On the third day, β€˜Q’ is replaced by β€˜R’, and again on the fourth day, β€˜P’ works alone. The process repeats in the same manner. Find the total time taken to complete the task. (Round off to two decimal places)
    A 6.59 days Correct Answer Incorrect Answer
    B 8.22 days Correct Answer Incorrect Answer
    C 2.96 days Correct Answer Incorrect Answer
    D None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the total work be the LCM of [10, 15, 20] = 60 units. Efficiency of β€˜P’ = 60/10 = 6 units/day. Efficiency of β€˜Q’ = 60/15 = 4 units/day. Efficiency of β€˜R’ = 60/20 = 3 units/day. Work done on the first day = 6 Γ— 1 = 6 units. Work done on the second day = (6 + 4) Γ— 1 = 10 units. Work done on the third day = (6 + 3) Γ— 1 = 9 units. Total work done in the first three days = 6 + 10 + 9 = 25 units. Remaining work = 60 – 25 = 35 units. Time taken to complete the remaining work = (6/6) + (10/10) + (9/9) + (10/17) β‰ˆ 3 + (10/17) β‰ˆ 3.59 days. Total time = 3 + 3.59 = 6.59 days.

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