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    Question

    'N,' 'V,' and 'R' have individual work completion times

    of 140 days, 112 days, and 80 days, respectively. They all started working together on a task, but after 12 days, 'N' left working, and 'R' also left the job 16 days before the task's completion. Calculate how many days 'V' worked on the task.
    A 45 days Correct Answer Incorrect Answer
    B 44 days Correct Answer Incorrect Answer
    C 35 days Correct Answer Incorrect Answer
    D 52 days Correct Answer Incorrect Answer
    E none of these Correct Answer Incorrect Answer

    Solution

    ATQ,   Let the total work be 560 units (LCM of 140, 112 and 80)   Amount of work done by N alone in one day = 560/140 = 4 units   Amount of work done by V alone in one day = 560/112 = 5 units   Amount of work done by R alone in one day = 560/80 = 7 units   Amount of work done by N, V and R together in 12 days = 12 × (4 + 5 + 7) = 192 units   Amount of work done by V alone in 16 days = 16 × 5 = 80 units   Remaining work = 560 – 192 – 80 = 288 units   Time taken by V and R together to complete 288 units work = 288/(7 + 5) = 24 days   So, the number days for which V worked = 12 + 16 + 24 = 52 days

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