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    A and B can do a piece of work in 8 days and 37 days, respectively. The number of days [Correct to one decimal place] required to complete the work if
    Question

    A and B can do a piece of work in 8 days and 37 days, respectively. The number of days [Correct to one decimal place] required to complete the work if both A and B work together is:

    A.

    7.7

    B.

    10.7

    C.

    7.1

    D.

    6.5

    Correct option is D

    Given: 

    A can complete a work = 8 days

    B can complete same work = 37 days 

    Formula Used: 

    Total work = Efficiency ×\times time

    Solution: 

    Total work = LCM (8, 37) = 296 

    Efficiency of A = 2968=37\frac{296}{8} = 37 

    Efficiency of B = 29637=8\frac{296}{37} = 8 

    Combined Efficiency = 8 + 37 = 45 

    Time taken by A + B:

    29645=6.57 days\frac{296}{45} = 6.57 \ days ​

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