Aarush asked Soham to take a two digit number and reverse it, then subtract the larger number from the smaller number. Soham did the same. This result will be always divisible by_____.

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Solution

The correct option is B 9
Let's consider a two digit number ab. Its general form will be $10 \times a + 1 \times b$ .
If we reverse it, then the number will become ba. Its general form will be $10 \times b + 1 \times a$ .
If we subtract both of the numbers, we get:
$(10 \times a + 1 \times b) - (10 \times b + 1 \times a)$
$= 9 (a - b)$

Observe that the result is a multiple of 9 and hence is exactly divisible by 9.

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