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    A can do a certain piece of work in 8 days, B can do the same work in 18 days and C an do the same work in 12 days. Find the number of days it will ta
    Question

    A can do a certain piece of work in 8 days, B can do the same work in 18 days and C an do the same work in 12 days. Find the number of days it will take to complete the same work, if they all work together.

    A.

    1948\frac{19}{48}​​

    B.

    7219\frac{72}{19}​​

    C.

    4819\frac{48}{19}​​

    D.

    1972\frac{19}{72}​​

    Correct option is B

    Given:

    A can do the work in 8 days.

    B can do the work in 18 days.

    C can do the work in 12 days.

    Solution: 

    Total rate of work = 
    18+118+112\frac18+\frac1{18}+\frac1{12} 

    To find the common denominator, LCM of 8, 18, and 12 = 72 

    Total rate of work = 972+472+672=1972\frac9{72}+\frac4{72}+ \frac6{72}= \frac{19}{72}

    Total time taken = 7219\frac{72}{19} days

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