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      Question

      Following questions have two quantities as Quantity I

      and Quantity II. You have to determine the relationship between them and give answer as  Quantity I: A, B and C can do a piece of work in 16, 32 and 48 days respectively. In how many days can A do the work if he is assisted by B and C on every fourth day?  Quantity II: A, B and C can do a piece of work in 12, 24 and 36 days respectively. In how many days work will be finished if they work on alternate days in the same order? 
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer
      D Quantity I ≄ Quantity II Correct Answer Incorrect Answer
      E Quantity I ≀ Quantity II Correct Answer Incorrect Answer

      Solution

      Quantity I:  Let total work = LCM of 16, 32 and 48 = 96 units  A's 1 day work = 6 units, B's 1 day work = 3 units & C's 1 day work = 2 units  Total work completed in 4 days = 6+6+6+(6+3+2) = 29 units  So total work completed in 12 days = 87 units  Total work in 13 days = 87 + 6 = 93 unit  Rest 3 unit is completed by A in = 3/6 days = 1/2 days  So total work completed in = 13 +(1/2) = 27/2 days.  Quantity II:   Let the total work = LCM of 12, 24 and 36 = 72 units  A's 1 day work = 6 units, B's 1 day work = 3 units & C's 1 day work = 2 units  Total work completed in 3 days = (6+3+2) = 11 units  Hence 11 units is completed in 3 days,  So 66 units will completed in = 3 × 6 = 18 days  Next day, A will come & will do 6 units more so workdone till now = 66 + 6 = 72 units  So total work completed in = 18 + 1 = 19 days.

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