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    A and B together can do a piece of the work in 50 hours, B and C together can do the same work in 75 hours and A and C together can do the same in 25
    Question

    A and B together can do a piece of the work in 50 hours, B and C together can do the same work in 75 hours and A and C together can do the same in 25 hours. Find the time in which A, B, and C together will complete the task.

    A.

    40011\frac{400}{11}​ hours

    B.

    15011\frac{150}{11}​ hours

    C.

    13111\frac{131}{11}​ hours

    D.

    30011\frac{300}{11}​ hours

    Correct option is D

    ​Given: 

    A and B together can complete the work in 50 hours  

    B and C together can complete the work in 75 hours  

    A and C together can complete the work in 25 hours  

    Solution: 

    A and B work rate = 150 \frac{1}{50}

    B and C work rate = 175 \frac{1}{75} 

    C and A work rate = 125 \frac{1}{25} 

    Now,  

    A + B + B + C + C + A = 150+175+125​\frac{1}{50} + \frac{1}{75} + \frac{1}{25} 

    2( A + B + C ) = 11150\frac{11}{150} 

    A + B + C  = 11300\frac{11}{300}​​

    The time taken by A, B, and C together to complete the work is the reciprocal of this rate

    Time = 30011 hours\frac{300}{11} \text{ hours}​​


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