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      Question

      A’ and β€˜B’ alone can do a certain work in 20 days

      and 30 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 110/3days Correct Answer Incorrect Answer
      B 120/7days Correct Answer Incorrect Answer
      C 121/7days Correct Answer Incorrect Answer
      D 154/3days Correct Answer Incorrect Answer
      E none of these Correct Answer Incorrect Answer

      Solution

      Total work = 60 units (LCM of 20 and 30) Efficiency of β€˜A’ = 60/20 = 3 units/day Efficiency of β€˜B’ = 60/30 = 2 units/day According to the question, β€˜A’ worked for β€˜x’ days and β€˜B’ worked for β€˜2x days. Therefore, 3x + 2 Γ— 2x = 120 Or 3x + 4x = 60 Or x = 60/7days total time taken to complete the whole work = 2Γ—60/7=120/7days

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