Question #f0641

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Answer 1 · 2017-03-10T00:50:28

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

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 $a=9-b$
$rarr a=4$