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      Question

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

      the new number becomes 8 less than 150% of the original number. If the sum of the digits is 7, find the original number.
      A 34 Correct Answer Incorrect Answer
      B 25 Correct Answer Incorrect Answer
      C 16 Correct Answer Incorrect Answer
      D 43 Correct Answer Incorrect Answer
      E 52 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 = 1.5 × (10x + y) − 8
      Multiplying both sides by 2, 
      20y + 2x = 30x + 3y − 16 
      ⇒ 28x − 17y = 16  …. (I)
      And, x + y = 7  …. (II)
      From (II), x = 7 − y. Substitute in (I): 
      28(7 − y) − 17y = 16 
      196 − 45y = 16 
      45y = 180 
      y = 4
      Then x = 3. 
      So, original number = 10 × 3 + 4 = 34.

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