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    Question

    A can complete a work in  9 days , and B can complete

    it in  18 days . They work together with C and complete the work in  3 days . In how many days can  C alone  complete the work?
    A 10 days Correct Answer Incorrect Answer
    B 12 days Correct Answer Incorrect Answer
    C 18 days Correct Answer Incorrect Answer
    D 21 days Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Assume total work = LCM(9, 18) = 18 units A’s rate = 18/9 = 2 units/day B’s rate = 18/18 = 1 unit/day Let C’s rate = x units/day Total rate = (2 + 1 + x) units/day = (3 + x) They finish in 3 days: (3 + x) × 3 = 18 9 + 3x = 18 3x = 9 → x = 3 units/day Time for C alone = 18 / 3 = 6 days

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