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      Question

      The cost of item A is 8 more than the sum of cost of B and

      C together. The ratio of cost of item B and C is 3:5 respectively. The cost of B is a multiple of 8 and is less than 90. The sum of cost of A and B together is defined as ₹P, when the cost of item C is between 50 and 100 and the difference between the cost of A and C is defined as ₹Q, when the cost of item C is more than or equal to 100.Which of the following can be true regarding P and Q?I: (P - Q - 4 ) is a square number.II: Sum of P and Q is more than 264.III: (3Q - P) is a multiple of 14.
      A Only I Correct Answer Incorrect Answer
      B Only III Correct Answer Incorrect Answer
      C Both I and II Correct Answer Incorrect Answer
      D Both I and III Correct Answer Incorrect Answer
      E All I, II and III Correct Answer Incorrect Answer

      Solution

      Let the cost of item B and C be 3x and 5x respectively.
      Since, the cost of B i.e. 3x is a multiple of 8 and is less than 90.
      Cost of B = ₹24 or ₹48 or ₹72
      Case I:
      When the cost of B = ₹24
      Cost of item C = 24*5/3 = ₹40 (which is less than 50)
      Case II:
      When the cost of B = ₹48
      Cost of item C = 48*5/3 = ₹80 (which is between 50 and 100)
      Cost of item A = 80 + 48 + 8 = ₹136
      P = sum of cost of A and B together = 136 + 48 = ₹184
      Case III:
      When the cost of B = ₹72
      Cost of item C = 72*5/3 = ₹120 (which is more than 100)
      Cost of item A = 72 + 120 + 8 = ₹200
      Q = difference between the cost of A and C = 200 - 120 = 80
      I: (P - Q) = 184 - 80 - 4 = 100 is a square number.
      II: Sum of P and Q = 184 + 80 = 264 is equal to 264.
      III: (3Q - P) = 3*80 - 184 = 56 is a multiple of 14.

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