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      Question

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

      the new number becomes 24 more than 180% of the original number. If the sum of the digits is 6, find the original number.
      A 51 Correct Answer Incorrect Answer
      B 24 Correct Answer Incorrect Answer
      C 15 Correct Answer Incorrect Answer
      D 33 Correct Answer Incorrect Answer
      E 42 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 = (9/5) × (10x + y) + 24

      Multiplying both sides by 5, 
      50y + 5x = 90x + 9y + 120 
      ⇒ 85x − 41y = −120  …. (I)

      And, x + y = 6  …. (II)

      From (II), x = 6 − y. Substitute in (I): 
      85(6 − y) − 41y = −120 
      510 − 126y = −120 
      126y = 630 
      y = 5

      Then x = 1. 
      So, original number = 10 × 1  + 5 = 15.

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