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      Question

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

      the new number becomes 19 less than 150% of the original number. If the sum of the digits is 11, find the original number.
      A 65 Correct Answer Incorrect Answer
      B 56 Correct Answer Incorrect Answer
      C 47 Correct Answer Incorrect Answer
      D 38 Correct Answer Incorrect Answer
      E 29 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) − 19
      Multiplying both sides by 2, 
      20y + 2x = 30x + 3y − 38 
      ⇒ 28x − 17y = 38  …. (I)
      And, x + y = 11  …. (II)
      From (II), x = 11 − y. Substitute in (I): 
      28(11 − y) − 17y = 38 
      308 − 45y = 38 
      45y = 270 
      y = 6
      Then x = 5. 
      So, original number = 10 × 5 + 6 = 56.

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