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    Question

    A alone can finish a piece of work in 10 days and B

    alone can finish it in 15 days. They work together for 3 days and the remaining work is finished by C in 4 days. In how many days can C alone finish the entire work?
    A 2 days Correct Answer Incorrect Answer
    B 5 days Correct Answer Incorrect Answer
    C 8 days Correct Answer Incorrect Answer
    D 10 days Correct Answer Incorrect Answer

    Solution

    ATQ, Let total work = 1 unit A’s 1-day work = 1/10 B’s 1-day work = 1/15 Together (A + B) 1-day work = 1/10 + 1/15 LCM of 10 and 15 = 30 = 3/30 + 2/30 = 5/30 = 1/6 Work done in 3 days = 3 × (1/6) = 1/2 So remaining work = 1 − 1/2 = 1/2 C finishes 1/2 work in 4 days C’s 1-day work = (1/2) / 4 = 1/8 So C alone would finish full work in 8 days.

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