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      Question

      'A' and 'B' alone can complete a work in 9 days and 18

      days, respectively. Find the time taken by them to complete the work if they work on alternate days starting with 'A'.
      A 17 days Correct Answer Incorrect Answer
      B 15 days Correct Answer Incorrect Answer
      C 12 days Correct Answer Incorrect Answer
      D 25 days Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let the total work be the LCM of 9 and 18, which is 18 units. Efficiency of 'A' = 18/9=2 units/day Efficiency of 'B' = 18/18=1 unit/day If the work was started by 'A', then on the first day, work completed by 'A' = 2 units On the next day, work completed by 'B' = 1 unit Therefore, in two days, the amount of work completed by 'A' and 'B' = 2 + 1 = 3 units So, in 12 days, work completed by 'A' and 'B' = 3 × 6 = 18 units Therefore, total time taken by them to complete the work = 12 days

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