A two-digit number is such that the product of the digits is 8. If 63 is added to this number, the digits interchange their places. What is the sum of the digits in the number?

Explanation

Let the number be 10x + y. We are given xy = 8 and (10x + y) + 63 = 10y + x, which simplifies to 9y - 9x = 63 \implies y - x = 7. The digits satisfying xy=8 and y-x=7 are x=1, y=8. The sum of the digits is 1 + 8 = 9.

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