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      Question

      Working alone, β€˜X’ and

      β€˜Y’ can complete a work in 16 days and 10 days, respectively. They started working together but after 4 days, β€˜Y’ was replaced by β€˜Z’ and the work got finished in the next 4 days. Find the time taken by β€˜Z’ alone to finish the whole work.
      A 38 days Correct Answer Incorrect Answer
      B 40 days Correct Answer Incorrect Answer
      C 48 days Correct Answer Incorrect Answer
      D 50 days Correct Answer Incorrect Answer

      Solution

      Let the total work be 80 units (LCM of 16 and 10).

      Combined efficiency of X and Y = 5+8=13 units/day. Work done by X and Y together in 4 days = 13Γ—4=52 units. Remaining work = 80βˆ’52=28 units.

      Efficiency of Z = 7βˆ’5=2 units/day.

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