Question

The difference of the number consisting of two digits and the number formed by interchanging the digits is always divisible by ? Explanation needed.​

Answer 1

Answer:

A two digit number can be written as 10x + y,

where x is the digit at tens' place and y is the digit at ones' place.

On interchanging the digits, the number formed

= 10x + y

Therefore,

10x + y - (10y + x) = 9x - 9y = 9(x - y)10x+y−(10y+x)=9x−9y=9(x−y)

=> Given difference is always divisible by 9.