Question

The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9 less than three times the original number. What is the original number? Thank you!

Answer 1

Number is `27`.

Explanation:

Let the unit digit be `x` and tens digit be `y`

then `x+y=9` ........................(1)

and number is `x+10y`

On reversing the digits it will become `10x+y`

As `10x+y` is `9` less than three times `x+10y`, we have

`10x+y=3(x+10y)-9`

or `10x+y=3x+30y-9`

or `7x-29y=-9` ........................(2)

Multiplying (1) by `29` and adding to (2), we get

`36x=9xx29-9=9xx28`

or `x=(9xx28)/36=7`

and hence `y=9-7=2`

and number is `27`.