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      Question

      β€˜X’ and β€˜Y’ can do a piece of work in 10 days

      and 25 days, respectively. β€˜X’ started working alone and was replaced by β€˜Y’ after 5 days. In how many days can β€˜Y’ complete the remaining amount of work alone?
      A 8 days Correct Answer Incorrect Answer
      B 10 days Correct Answer Incorrect Answer
      C 12.5 days Correct Answer Incorrect Answer
      D 15 days Correct Answer Incorrect Answer

      Solution

      Let the total work be 200 units (LCM of 10 and 25) Efficiency of β€˜X’ = 200/10 = 20 units/day Efficiency of β€˜Y’ = 200/25 = 8 units/day Let the number of days taken by β€˜Y’ to finish the remaining amount of work be β€˜x’ ATQ, (20 Γ— 5) + 8x = 200 Or, 8x = 200 – 100 Or, 8x = 100 Or, x = 100/8 = 12.5 Therefore, time taken by β€˜Y’ to complete the remaining work alone = 12.5 days

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