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    Question

    6 women and 4 children can complete a piece of work in

    12 days. If 3 more women join them, they can finish 3/5 of the work in 6 days. Find the time taken by 18 women to complete the entire work.
    A 16 days Correct Answer Incorrect Answer
    B 28 days Correct Answer Incorrect Answer
    C 10 days Correct Answer Incorrect Answer
    D 17 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    (6W + 4C) ├Ч 12 = (6W + 4C + 3W) ├Ч [1/(3/5)] ├Ч 6

    (72W + 48C) = (9W + 4C) ├Ч (5/3) ├Ч 6

    (9W + 4C) ├Ч 10 = 90W + 40C

    So, 72W + 48C = 90W + 40C

    48C - 40C = 90W - 72W

    8C = 18W

    1W = (8/18)C = (4/9)C

    Now convert all to C:

    (6W + 4C) = (6 ├Ч 4/9 + 4)C = (24/9 + 4)C = (24 + 36)/9 = 60/9 = 20/3 C

    Work = (20/3 C) ├Ч 12 = 80C

    Now, 18W = 18 ├Ч (4/9)C = 8C

    So, time = 80C / 8C = 10 days

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