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    Question

    A can do a piece of work in 12 days, while B

    alone can do it in 18 days. They work together for 6 days and the rest of the work is completed by C in 4 days. If they get Rs. 720 for the whole work, how should they divide the money?
    A Rs. 300, Rs. 200, Rs. 220 Correct Answer Incorrect Answer
    B Rs. 360, Rs. 140, Rs. 220 Correct Answer Incorrect Answer
    C Rs. 300, Rs. 240, Rs. 180 Correct Answer Incorrect Answer
    D Rs. 360, Rs. 240, Rs. 120 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Work done by A and B in 6 days = (1/12 + 1/18) × 6 = 5/6 Work remaining = 1 - 5/6 = 1/6 ∴ C alone can do the work in 6 × 4= 24 days Ratio of their share work = 6/12 : 6/18 : 4/24 = 3:2:1 Share of A’s wages = 3/6 × 720 = Rs. 360 Share of B’s wages = 2/6 × 720 = Rs. 240 Share of C’s wages = 1/6 × 720 = Rs. 120 Alternate Method: A B Time taken 12 18 Total work = LCM 36 units 3 : 2 ATQ, A+B's work in 6 days = (3+2)`xx` 6 = 30 units So remainning work = 36 - 30 = 6units which is completed by C alone in 4days So C's 1 day work = 6/(4)=1.5units Hence ratio of work done of A, B & C = 3 `xx` 6 : 2 `xx` 6 : 6 = 18 : 12:6 = 3:2:1

    Share of A’s wages = 3/6 × 720 = Rs. 360
    Share of B’s wages = 2/6 × 720 = Rs. 240 Share of C’s wages = 1/6 × 720 = Rs. 120

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