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    Question

    β€˜P’, β€˜Q’ and β€˜R’ can finish a task in 12

    days, 36 days and 72 days respectively. β€˜P’ and β€˜Q’ begin the task. After β€˜n’ days, β€˜P’ leaves and β€˜R’ joins β€˜Q’. If the total work is completed in 20 days, find the value of 2n.
    A 2.5 Correct Answer Incorrect Answer
    B 4.8 Correct Answer Incorrect Answer
    C 12.5 Correct Answer Incorrect Answer
    D 10.5 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the total work be 72 units (LCM of 12, 36, 72) Efficiency of β€˜P’ = 72 / 12 = 6 units/day Efficiency of β€˜Q’ = 72 / 36 = 2 units/day Efficiency of β€˜R’ = 72 / 72 = 1 unit/day ATQ, (6 + 2) Γ— n + (2 + 1) Γ— (20 - n) = 72 Or, 8n + 3(20 - n) = 72 Or, 8n + 60 - 3n = 72 Or, 5n = 12 Or, n = 2.4 Required value = 2 Γ— 2.4 = 4.8

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