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      Question

      A two-digit number has a sum of its digits equal to 12.

      Additionally, if 45 is subtracted from this number, the resulting number has its digits reversed. What is the original number?
      A 53 Correct Answer Incorrect Answer
      B 93 Correct Answer Incorrect Answer
      C 83 Correct Answer Incorrect Answer
      D 75 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      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 = 12 --------- (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 = 12 + 5

      Or, 2b = 17

      Or, 'b' = 7

      On putting value of 'b' in equation I,

      We get, 7 + a = 12

      Or, 'a' = 5

      Required number = 10 × 7 + 5 = 75

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