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      Question

      'Amit' can complete a project in 20 days while 'Bhavya' can

      do it in 30 days alone. Bhavya starts the project on Day 1, then Amit works on Day 2, and both work together on Day 3. They follow this sequence repeatedly. How many days will they take to complete the project?
      A 24 days Correct Answer Incorrect Answer
      B 18 days Correct Answer Incorrect Answer
      C 12 days Correct Answer Incorrect Answer
      D 10 days Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let the total work be LCM (20, 30) = 60 units

      Efficiency of Amit = 60 / 20 = 3 units/day

      Efficiency of Bhavya = 60 / 30 = 2 units/day

      Work done in 3 days = Bhavya (2Ă—1) + Amit (3Ă—1) + Both (5Ă—1) = 2 + 3 + 5 = 10 units

      In 3Ă—5 = 15 days (5 full cycles), work = 10 Ă— 5 = 50 units

      Remaining work = 60 - 50 = 10 units

      Next 2 days work = Bhavya (2) + Amit (3) = 5 units

      Remaining = 10 - 5 = 5 units

      Next day (both) do 5 units → full day

      Total time = 15 (full cycles) + 2 + 1 = 18 days

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