Call that number is \(\overline{ab}\)

Following the thread we have :

\(\left\{{}\begin{matrix}a+b=\dfrac{\overline{ab}}{6}\\ab+25=\overline{ba}\end{matrix}\right.\)

Now we just calculate a and b then we'll find the answer :)

\(\Leftrightarrow\left\{{}\begin{matrix}a+b=\dfrac{10a+b}{6}\\ab+25=10b+a\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6a+6b=10a+b\\ab+25=10b+a\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}5b=4a\\ab+25=10b+a\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=\dfrac{4a}{5}\\a\cdot\dfrac{4a}{5}+25=10\cdot\dfrac{4a}{5}+a\end{matrix}\right.\)

Solve the second expression we have a = 5.

So \(b=\dfrac{4a}{5}=\dfrac{4\cdot5}{5}=4\)

So the number \(\overline{ab}\) is 54.