Find the number

Let $t$ be the tens’ digit and $u$ be the units’ digit. Then the number is,

$10t+u$

If the digits are reversed, the new number is

$10u+t$

From the problem,

$t+u=9$ $\implies$ $\boxed{u=9-t}$ $\color{#D61F06}(1)$

and

$10u+t=3(10t+u)-9$ $\implies$ $10u+t=30t+3u-9$ $\implies$ $\boxed{7u-29t=-9}$ $\color{#D61F06}(2)$

Substitute $\color{#D61F06}(1)$ in $\color{#D61F06}(2)$ , we have

$7(9-t)-29t=-9$

$63-7t-29t=-9$

$-36t=-72$

$t=2$

It follows that

$u=9-2=7$

Therefore, the number is $27$ .