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      Question

      The sum of the digits of a two-digit number is 7. If 45 is

      subtracted from this number, the digits reverse their positions. What is the original number?
      A 61 Correct Answer Incorrect Answer
      B 16 Correct Answer Incorrect Answer
      C 25 Correct Answer Incorrect Answer
      D 52 Correct Answer Incorrect Answer

      Solution

      Let ones and tens digit of the number be 'a' and 'b' respectively.
      So, original number = 10b + a
      Reverse number = 10a + b
      So, a + b = 7 --------- (I)
      And, 10b + a - 45 = 10a + b
      Or, 9b - 9a = 45
      Or, b - a = 5 ---------- (II)
      On adding equation I and II,
      We get, a + b + b - a = 7 + 5
      Or, 2b = 12
      Or, 'b' = 6
      On putting value of 'b' in equation I,
      We get, 6 + a = 7
      Or, 'a' = 1
      Required number = 10 x 6 + 1 = 61

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