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      Question

      ‘R’ and ‘S’ can do a piece of work in 20 days

      and 30 days, respectively. ‘R’ started working alone and was replaced by ‘S’ after 10 days. In how many days can ‘S’ complete the remaining amount of work alone?
      A 10 days Correct Answer Incorrect Answer
      B 8 days Correct Answer Incorrect Answer
      C 15 days Correct Answer Incorrect Answer
      D 12 days Correct Answer Incorrect Answer

      Solution

      Let the total work be 60 units (LCM of 20 and 30) Efficiency of ‘R’ = 60/20 = 3 units/day Efficiency of ‘S’ = 60/30 = 2 units/day Let the number of days taken by ‘S’ to finish the remaining amount of work be ‘x’ ATQ, (3 × 10) + 2x = 60 Or, 2x = 60 – 30 Or, 2x = 30 Or, x = 30/2 = 15 Therefore, time taken by ‘S’ to complete the remaining work alone = 15 days

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