Pick a two digit number with distinct digits. Now, reverse the digits. Subtract the smaller number from the larger number. The sum of the digits of the difference obtained is always ____.

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Solution

The correct option is D
9

Let the two digit number be $10 A + B$ and its reverse will be $10 B + A$
Subtraction of these numbers would yield $9 (A - B)$ or $9 (B - A)$ .
In either way, the number thus obtained will be multiple of 9 and the whole number is divisible by 9.
Therefore, the sum of all digits of the number should be 9 or multiple of 9.
The digits of the difference will be less than 9.Therefore, the sum of these digits will always be 9.

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