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    A and B together can complete a piece of work in 25 days, B and C together can complete the same piece of work in 36 days, while C and A together can
    Question

    A and B together can complete a piece of work in 25 days, B and C together can complete the same piece of work in 36 days, while C and A together can complete it in 30 days. If A, B, C, and D together can complete this piece of work in 18 days, then in how many days can D alone complete this piece of work?

    A.

    210

    B.

    180

    C.

    200

    D.

    225

    Correct option is C

    Given:

    A and B together can complete the work in 25 days.

    B and C together can complete the work in 36 days.

    C and A together can complete the work in 30 days.

    A, B, C, and D together can complete the work in 18 days.

    Solution:

    Work rate of A + B =125= \frac{1}{25}​​

    Work rate of B + C =136= \frac{1}{36}​​

    Work rate of C + A =130 \frac{1}{30}​​

    Work rate of A + B + C + D =118 \frac{1}{18}​​

    Now, 

    (A + B) + (B + C) + (C + A) =125+136+130 \frac{1}{25} + \frac{1}{36} + \frac{1}{30}

    2A + 2B + 2C =125+136+130 \frac{1}{25} + \frac{1}{36} + \frac{1}{30}​​

    2(A + B + C) =721800+501800+601800=1821800 \frac{72}{1800} + \frac{50}{1800} + \frac{60}{1800} = \frac{182}{1800}

    A+B+C=12×1821800=911800A + B + C= \frac{1}{2} \times \frac{182}{1800} = \frac{91}{1800}........(1)

    A + B + C + D =118= \frac{1}{18}........(2) 

    Subtracting (1) and (2), we get

    D =118911800 \frac{1}{18} - \frac{91}{1800}

    D = 1001800911800=91800=1200\frac{100}{1800} - \frac{91}{1800} = \frac{9}{1800} = \frac{1}{200}

    The rate of work of D is 1200\frac{1}{200}​, meaning D can complete the work in 200 days.

    Alternate Method:

    ​Efficiency of A + B + C =36+25+302=912=45.5\frac{36+25+30}2=\frac{91}2=45.5

    ​​Efficiency of D = 50 - 45.5 = 4.5

    Work done by D =9004.5=200\frac{900}{4.5}=200 days​

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