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    A and B can together complete a task in 16 days. They started a task together, and after 4 days A leave, B takes 24 days to finish the rest of the tas
    Question

    A and B can together complete a task in 16 days. They started a task together, and after 4 days A leave, B takes 24 days to finish the rest of the task. How many days would B have taken to do the task if he worked alone?

    A.

    30 days

    B.

    24 days

    C.

    32days

    D.

    34 days

    Correct option is C

    Given:
    A and B can together complete a task in 16 days
    They started a task together and after 4 days A leave, B takes 24 days to finish the rest of the task.
    Formula Used:
    Work = Time × Efficiency
    Solution:
    Let the efficiency of A and B be a and b respectively.
    Total work = (a + b) × 16
    Work done by A and B together = 4 × (a + b)
    Remaining work done by B = 24 × b  

    Total work = work done by A + B together in 16 days = work done by ( A + B) × 4 + work done by B in 24 days 

    So,   
    4 × (a + b) + 24 × b = (a + b) × 16
    a = b
    Then, time taken by B alone to finish work =(1+1)×161\frac{(1 + 1) \times 16}{1}​ = 32 days.

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