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    A and B can do a piece of work in 4 days and 46 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 4 days and 46 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.

    6.9

    B.

    5.5

    C.

    3.6

    D.

    6.8

    Correct option is C

    Given:

    A can complete the work in 4 days.

    B can complete the work in 46 days.

    Formula Used:

    Time = 1Rate of A+Rate of B\frac{1}{\text{Rate of A} + \text{Rate of B}}

    Solution:

    Rate of A = 14\frac{1}{4}​ (since A completes the work in 4 days)

    Rate of B = 146\frac{1}{46}​ (since B completes the work in 46 days)

    Time = Time=114+146\text{Time} = \frac{1}{\frac{1}{4} + \frac{1}{46}}

    14+146=46+44×46=50184\frac{1}{4} + \frac{1}{46} = \frac{46 + 4}{4 \times 46} = \frac{50}{184}

    Time = 150184=18450\frac{1}{\frac{50}{184}} = \frac{184}{50}​ = 3.68 days

    Thus, 3.6 days 

    Alternate Method: 

    Total Work = 92 

    Total Efficiency = 23+2 = 25 

    Total time = 9225=3.6\frac{92}{25} = 3.6 Days ​

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