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      Question

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

      the new number becomes 2 more than 200% of the original number. If the sum of the digits is 7, find the original number.
      A 52 Correct Answer Incorrect Answer
      B 34 Correct Answer Incorrect Answer
      C 25 Correct Answer Incorrect Answer
      D 61 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 = 2 × (10x + y) + 2 
      10y + x = 20x + 2y + 2 
      ⇒ 19x − 8y = −2  …. (I)

      And, x + y = 7  …. (II)

      From (II), y = 7 − x. Substitute in (I): 
      19x − 8(7 − x) = −2 
      27x = 54 
      x = 2

      Then y = 7 − 2 = 5. 
      So, original number = (10 × 2 + 5) = 25.

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