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Discussion :: Time and Work

  1. A contractor undertakes to complete a work in 120 days with the help of 100 workers. After 45 days, he finds that only ¼ of the work has been completed. To complete the remaining work, how many extra workers will be required?
    2. A.
    80 workers
    B.
    180 workers
    C.
    160 workers
    D.
    100 workers

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    Answer : Option A

    Explanation :

    Apply formula: [Man1 * day1* hour1*]/ work1 = [Man2 * day2* hour2*]/ work2

    ATQ, target = 120 days

    M1 = 100, M2 =?
    D1 = 45, D2 = 120-45 = 75
    Let total work = 1
    W1 = ¼, W2= 1-1/4 = ¾
    Assume H1 = H2 = 1

    Now, apply the formula

    [M1 * D1 * H1]/ W1 = [M2 * D2 * H2]/ W2
    Now, [H1 = H2 = 1]
    So, [M1 * D1 * W2] = [M2 * D2 * W1]

    Or, (100 * 45 * 3/4) = (M2 * 75 * ¼)
    Or, M2 = 180

    So, M2 - M1 = 180 -100 = 80 extra workers will be required.

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