Question

The sum of the in a two digit number is 17. lf the digits are reversed, the new digits number will be 9 less than the original number. What is the original number?

Answer 1

The number is `98`

Explanation:

Let the number be `10x+y`

So we can write

`x+y=17`------------------------------Eq `1`

Reverse of the number will be `10y+x`

So we can write

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

or

`9x-9y=9`

or

`9(x-y)=9`

or

`x-y=9/9`

or

`x-y=1`-------------------Eq `2`

Adding up the Eq `1` and Eq `2`

we get

`x+y+x-y=17+1`

or

`2x+0=18`

or

`2x=18`

or

`x=18/2`

or

`x=9`

By plugging the value `x=9` in the `x+y=17`

We get

`9+y=17`

or

`y=17-9`

or

`y=8`

Therefore the number is `98`