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      Question

      β€˜A’ and β€˜B’ alone can do a certain work in 30

      days and 40 days, respectively. Both started the work together but after β€˜x’ days β€˜A’ left the work and the rest work was completed by B alone in β€˜2x’ days. Find the total time taken to complete the whole work in this way.
      A 28days Correct Answer Incorrect Answer
      B 12days Correct Answer Incorrect Answer
      C 27.69days Correct Answer Incorrect Answer
      D 48days Correct Answer Incorrect Answer

      Solution

      Total work = 120 units (LCM of 30 and 40) Efficiency of β€˜A’ = 120/30 = 4 units/day Efficiency of β€˜B’ = 120/40 = 3 units/day According to the question, β€˜A’ worked for β€˜x’ days and β€˜B’ worked for β€˜2x days. Therefore, (4+3)x + 3 Γ— 2x = 120 Or 7x + 6x = 120 Or x = 120/13 total time taken to complete the whole work = 3Γ—120/13 =360/13 days =27.69days

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