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.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 → y = 5. Substitute y = 5 into x + y = 12: x + 5 = 12 → x = 7. The original number is 10x + y = 10(7) + 5 = 75. Correct answer: d. 75
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