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      Question

      A two-digit number is such that the sum of its digits is

      12. If the number formed by reversing its digits is 18 less than the original number, find the original number.
      A 39 Correct Answer Incorrect Answer
      B 48 Correct Answer Incorrect Answer
      C 57 Correct Answer Incorrect Answer
      D 75 Correct Answer Incorrect Answer

      Solution

      Let the original number be 10x + y, where x is the tens digit and y is the units digit. Given: x + y = 12 and 10y + x = (10x + y) - 18. Simplify the second condition: 10y + x = 10x + y - 18 9y - 9x = -18 y - x = -2. Now solve the two equations: x + y = 12 y - x = -2. Add the equations: 2y = 10 тЖТ y = 5. Substitute y = 5 into x + y = 12: x + 5 = 12 тЖТ x = 7. The original number is 10x + y = 10(7) + 5 = 75. Correct answer: d. 75

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