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  1. #1
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    work problem

    A is twice as good a workman as B and together they finish a piece of work in 18 days.in how many days will A alone finish this work?
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  2. #2
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    Quote Originally Posted by neha1 View Post
    A is twice as good a workman as B and together they finish a piece of work in 18 days.in how many days will A alone finish this work?
    Lets suppose that worker A works finishes a job in A days

    and worker B finishes a job in B days

    Then worker A's rate is \frac{1}{A}

    Then worker B's rate is \frac{1}{B}

    But we know that worker A is "twice" as good (2 times as fast) as worker B

    so \frac{1}{A}=2\cdot \frac{1}{B}

    We can now set the rates equal

    \frac{1}{A}+\frac{1}{B}=\frac{1}{18}

    2\cdot \frac{1}{B}+\frac{1}{B}=\frac{1}{18}

    \frac{3}{B}=\frac{1}{18} \iff 54=B

    Plugging in and solving for A gives A=27.

    I hope this helps
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