Question

Take a two-digit number ab and reverse its digits. If the difference between ab and the new number is cd, then by which number is cd divisible?

• A. 9

Answer 1

The correct option is A 9

Let a 2-digit number be ab.
Then, original number = 10a + b
Number obtained by reversing the digits = 10b + a

The difference between the original number and the number formed after reversing the digits is cd.

$\therefore$ cd
= (10a + b) - (10b + a)
= 9(a - b)

As cd is a multiple of 9, it is always divisible by 9.