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    Question

    'Amit' can complete a project in 20 days while 'Bhavya' can

    do it in 30 days alone. Bhavya starts the project on Day 1, then Amit works on Day 2, and both work together on Day 3. They follow this sequence repeatedly. How many days will they take to complete the project?
    A 24 days Correct Answer Incorrect Answer
    B 18 days Correct Answer Incorrect Answer
    C 12 days Correct Answer Incorrect Answer
    D 10 days Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the total work be LCM (20, 30) = 60 units

    Efficiency of Amit = 60 / 20 = 3 units/day

    Efficiency of Bhavya = 60 / 30 = 2 units/day

    Work done in 3 days = Bhavya (2×1) + Amit (3×1) + Both (5×1) = 2 + 3 + 5 = 10 units

    In 3×5 = 15 days (5 full cycles), work = 10 × 5 = 50 units

    Remaining work = 60 - 50 = 10 units

    Next 2 days work = Bhavya (2) + Amit (3) = 5 units

    Remaining = 10 - 5 = 5 units

    Next day (both) do 5 units → full day

    Total time = 15 (full cycles) + 2 + 1 = 18 days

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