Question

    A man, a woman, a boy, and a girl can complete a certain

    task individually in 84 days, 105 days, 140 days, and 210 days respectively. How long will it take for all four of them working together to complete the task?
    A 21 days Correct Answer Incorrect Answer
    B 30 days Correct Answer Incorrect Answer
    C 28 days Correct Answer Incorrect Answer
    D 36 days Correct Answer Incorrect Answer

    Solution

    Let the total work = L.C.M of 84, 105, 140, and 210 = 420 units
    Efficiency of a man = 420 ÷ 84 = 5 units/day
    Efficiency of a woman = 420 ÷ 105 = 4 units/day
    Efficiency of a boy = 420 ÷ 140 = 3 units/day
    Efficiency of a girl = 420 ÷ 210 = 2 units/day
    So, time taken by a man, a woman, a boy and a girl working together = 420 ÷ (5 + 4 + 3 + 2) = 30 days

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