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    Question

    138 unit of work can be completed by P alone in 23 days.

    P started working alone and joined by Q after 11 days such that they completed the remaining work in 8 days. Find the number of days taken by Q to complete the whole work alone.
    A 37.5 days Correct Answer Incorrect Answer
    B 46 days Correct Answer Incorrect Answer
    C 13.5 days Correct Answer Incorrect Answer
    D 14 days Correct Answer Incorrect Answer
    E 12 days Correct Answer Incorrect Answer

    Solution

    Let the efficiency of Q = x units/day Efficiency of P = (138/23) = 6 units/day According to question: 6 × 11 + (6 + x) × 8 = 138 Or, 66 + 48 + 8x = 138 Or, 8x = 138 – 114 Or, 8x = 24 Or, x = 3 Number of days taken by Q to complete the work alone = (138/3) = 46 days

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