Question

Show that the difference of a two digit number and the number obtained by

reversing digits is a multiple of 9.​

Answer 1

Step-by-step explanation:

Given:-

A two digit number

To show:-

Show that the difference of a two digit number and the number obtained by reversing digits is a multiple of 9.

Solution:-

Let the digits in a two digit number be X and Y

Let X be in the 10's place in the number then

Place Value of X = 10×X = 10X

Let Y be in the 1's place in the number then

Place Value of Y =Y×1 = Y

Now the two digit number = 10X +Y

If the digits are reversed by their places then the number obtained by the reversing the digits =

10Y +X

The difference between the original number and the number obtained by reversing the digits

=>(10X+Y) - (10Y+X)

=>10X+Y-10Y-X

=>(10X-X)+(Y-10Y)

=>9X -9Y

=>9(X-Y)

=>9 multiple

The difference is a multiple of 9

Answer:-

The difference of a two digit number and the number obtained by reversing digits is a multiple of 9.

Check :-

Consider any two digit number 81

Number obtained by the reversing digits = 18

Their difference = 81-18 = 63 = 9×7

Multiple of 9

and

A two digit number = 52

The number obtained by the reversing digits = 25

Their difference = 52-25

=>27

=>9×3

=>Multiple of 9

Verified the given relations.