Question

Question #f0641

Answer 1

Original number: `color(green)(45)`

Explanation:

If `a` is the tens digit and `b` is the units digit.
The original number is `10a+b`
and the number with the digits reversed is `10b+a`

Since the number with the digits reversed is `9` more than the original number:
`(10b+a) -(10a+b)=9`

`rarr 9b-9a=9`

`rarr b-a=1`

`rarr a=b-1`

We are also told that
`a+b=9 rarr a=9-b`

So
`b-1=9-b`

`rarr 2b=10`

`rarr b=5`

and since `a=9-b`
`rarr a=4`