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    X can complete a task in 15 days, and Y can complete the same task in 20 days. If X and Y work on alternate days starting with X, in how many days wil
    Question

    X can complete a task in 15 days, and Y can complete the same task in 20 days. If X and Y work on alternate days starting with X, in how many days will the work be completed?

    A.

    17

    B.

    22

    C.

    15

    D.

    19

    Correct option is A

    Given:
    X can do 60 units in 15 days
    Y can do 60 units in 20 days 
    Formula Used:
    Efficiency=Total WorkTotal Time Taken\text{Efficiency} = \frac{\text{Total Work}}{\text{Total Time Taken}}​​
    Solution:
    Total work = LCM of 15 and 20 = 60 units
    X can do 60 units in 15 days
    → X's 1-day work = 60 ÷ 15 = 4 units/day
    Y can do 60 units in 20 days
    → Y's 1-day work = 60 ÷ 20 = 3 units/day
    Work done in 2 days (X + Y working alternate days) = 4 + 3 = 7 units
    In 16 days (8 cycles), total work = 7 ×8  = 56 units
    Work done in 16 days = 56 units
     Remaining work = 60 – 56  = 4 units
    Now, 4 unit remaining work will be completed by X on 17th day. 
    Total time to complete whole work = 16+ 1= 17 days


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