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    Question

    'A' and 'B' can complete a piece of work in 10 days, 'B'

    and 'C' can complete the work in 16 days, and 'A' and 'C' can complete the work in 20 days. Find the time taken by 'B' to complete 50% of the work. (Answer should be rounded off to the nearest integer)
    A 10 days Correct Answer Incorrect Answer
    B 13 days Correct Answer Incorrect Answer
    C 12 days Correct Answer Incorrect Answer
    D 9 days Correct Answer Incorrect Answer

    Solution

    ATQ, Let the total work be 80 units (LCM of 10, 16, and 20). Combined efficiency of 'A' and 'B' =(80/10) = 8 units/day Combined efficiency of 'B' and 'C' = (80/16) =5 units/day Combined efficiency of 'A' and 'C' =(80/20) = 4 units/day So, combined efficiency of 'A', 'B', and 'C' = [(8+5+4)/2] = 8.5 units/day And, efficiency of 'B' = 8.5 - 4 = 4.5 units/day Therefore, required time ={(0.5×80)/4.5} = 9 days

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