Question

Aarush asked Soham to take a number and reverse it, then subtract the larger number from the smaller number. The result is exactly divisible by 9. State true or false

• A. Not divisible by 9
• B. Divisible by 9

Answer 1

The correct option is A

Not divisible by 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.
Similarly, for 3 digit numbers, the difference of the number and number obtained by reversing the digits (if abc is the number) will be given by:
$(100\times a+10\times b+c)-(100\times c+10\times b+a)=99(a-c)$
which is divisible by 9.