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    A works 5.4 times as fast as B, and A takes 22 days less than B to complete the job when each works alone. Calculate the number of days taken to compl
    Question

    A works 5.4 times as fast as B, and A takes 22 days less than B to complete the job when each works alone. Calculate the number of days taken to complete the same job if A and B work together.

    A.


    B.


    C.


    D.

    Correct option is C

    Given: 
    Efficiency of A = 5.4 Efficiency of B 
    A's time = B's time - 22 days
    Concept Used: 
    Time taken to complete the work is inversely proportional to the efficiency
    Time1 Efficiency\propto \frac{1}{\text { Efficiency}}​  
    if A complete the work in X days and B completes the work in Y days then
    together they can  work in one day =1X+1Y\frac{1}{X}+\frac{1}{Y} 
    Solution: 
    Efficiency of AEfficiency of B=5410=275\frac{\text{Efficiency of A}}{\text{Efficiency of B}} = \frac{54}{10} = \frac{27}{5} 
    Now , Time taken by ATime taken by B=527\frac{\text{Time taken by A}}{\text{Time taken by B}} = \frac{5}{27} 
    let time taken by A = 5x and time taken by b = 27x 
    27x - 5x = 22
    22x = 22
    x = 1 
    So, A's time to complete the work = 5 days, B's time to complete the work = 27 days
    A's work rate = 15\frac{1}{5}  ,  B's work rate = 127\frac{1}{27} 
    One day work by A and B = 15+127=27+5135=32135\frac{1}{5} + \frac{1}{27} = \frac{27 + 5}{135} = \frac{32}{135} 
    \therefore time taken to complete the work by A and B = 13532=4732days\frac{135}{32} = 4\frac{7}{32}days 
    Alternate Method:

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