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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 resulting number has its digits reversed. Determine the original number.
      A 61 Correct Answer Incorrect Answer
      B 52 Correct Answer Incorrect Answer
      C 16 Correct Answer Incorrect Answer
      D 25 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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