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      Question

      ‘A’ and ‘B’ alone can do a certain work in 30

      days and 40 days, respectively. Both started the work together but after ‘x’ days ‘A’ left the work and the rest work was completed by B alone in ‘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 ‘A’ = 120/30 = 4 units/day Efficiency of ‘B’ = 120/40 = 3 units/day According to the question, ‘A’ worked for ‘x’ days and ‘B’ worked for ‘2x days. Therefore, (4+3)x + 3 × 2x = 120 Or 7x + 6x = 120 Or x = 120/13 total time taken to complete the whole work = 3×120/13 =360/13 days =27.69days

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