Question

The sum of the digits in a two digit number is 10. if the digits are reversed, the new number will be 54 more than the original number. What is the original number?

Answer 1

`28`

Explanation:

Suppose the digits are `a` and `b`.

The original number is `10a+b`

The reversed number is `a+10b`

We are given:

`a+b = 10`

`(a+10b) - (10a+b) = 54`

From the second of these equations we have:

`54 = 9b - 9a = 9(b-a)`

Hence `b-a = 54/9 = 6`, so `b = a+6`

Substituting this expression for `b` into the first equation we find:

`a+a+6 = 10`

Hence `a=2`, `b = 8` and the original number was `28`