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    Question

    ‘P’, ‘Q’ and ‘R’ can finish a task in 12

    days, 36 days and 72 days respectively. ‘P’ and ‘Q’ begin the task. After ‘n’ days, ‘P’ leaves and ‘R’ joins ‘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 ‘P’ = 72 / 12 = 6 units/day Efficiency of ‘Q’ = 72 / 36 = 2 units/day Efficiency of ‘R’ = 72 / 72 = 1 unit/day ATQ, (6 + 2) × n + (2 + 1) × (20 - n) = 72 Or, 8n + 3(20 - n) = 72 Or, 8n + 60 - 3n = 72 Or, 5n = 12 Or, n = 2.4 Required value = 2 × 2.4 = 4.8

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