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      Question

      When the digits of a two-digit number are interchanged,

      the new number becomes 11 more than 120% of the original number. If the sum of the digits is 8, find the original number.
      A 53 Correct Answer Incorrect Answer
      B 44 Correct Answer Incorrect Answer
      C 35 Correct Answer Incorrect Answer
      D 62 Correct Answer Incorrect Answer

      Solution

      Let the unit digit and tens digit of the original number be ‘y’ and ‘x’, respectively.
      Original number = (10x + y)

      According to the data given: 
      10y + x = 1.2 × (10x + y) + 11

      Multiplying both sides by 5, 
      50y + 5x = 60x + 6y + 55 
      ⇒ 55x − 44y = −55  …. (I)

      And, x + y = 8  …. (II)

      From (II), x = 8 − y. Substitute in (I): 
      55(8 − y) − 44y = −55 
      440 − 99y = −55 
      99y = 495 
      y = 5

      Then x = 8 − 5 = 3. 
      So, original number = (10 × 3 + 5) = 35.

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