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      Question

      A and B alone can complete a work in 20 and 30 days,

      respectively. 50% of the work is completed by C in 5x days, and the remaining work is completed by A and B working together in ‘x’ days. Find the time taken by B and C to complete the whole work while working together.
      A 12 days Correct Answer Incorrect Answer
      B 10 days Correct Answer Incorrect Answer
      C 40 days Correct Answer Incorrect Answer
      D 20 days Correct Answer Incorrect Answer
      E 16 days Correct Answer Incorrect Answer

      Solution

      Time taken by A and B to complete the whole work while working together = (20 × 30)/(20 + 30) = 12 days
      So, x = 12/2 = 6 (Since, 50% of the work is done by A and B together)
      As, time taken by C to complete 50% of the work = 6 × 5 = 30 days
      So, time taken by C to complete the entire work = 30 × 2 = 60 days
      Therefore, time taken by B and C to complete the whole work while working together = (30 × 60)/(30 + 60) = 20 days

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