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    If machine A and B can produce 1100 units in 9 h and 12 h respectively. In how many hours can machine A and B working together at these constant rates
    Question

    If machine A and B can produce 1100 units in 9 h and 12 h respectively. In how many hours can machine A and B working together at these constant rates produce 1100 units?

    A.

    367\frac{36}7​​

    B.

    377\frac{37}7​​

    C.

    397\frac{39}7​​

    D.

    387\frac{38}7​​

    Correct option is A

    Given:
    Machine A produces 1100 units in 9 hours.​​
    Machine B produces 1100 units in 12 hours.

    Formula Used:

    Time=Total WorkCombined Rate\text{Time} = \frac{\text{Total Work}}{\text{Combined Rate}}

    Solution:

    ​Work rate of machine A  = 11009\frac{1100 }{9 }​ = 122.22 units/hour

    Work rate of machine B = 110012\frac{1100}{12}​ = 91.67 units/hour

    Combined work rate = 122.22 + 91.67  = 213.89 units/hour

    Time = 1100213.89 \frac{1100}{213.89 } ​= 367 \frac{36}{7}​ hours

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