[tex]\it \dfrac{\overline{ab}}{\overline{ba}} =\dfrac{3}{8} \Rightarrow 8\overline{ab}=3\overline{ba} \Rightarrow 8(10a+b) =3(10b+a) \Rightarrow
\\\;\\
\Rightarrow \it80a+8b=30b+3a \Rightarrow 77a = 22b|_{:11} \Rightarrow 7a = 2b \Rightarrow
\\\;\\
\Rightarrow \it a=2,\ \ b= 7[/tex]
Deci, numărul cerut este 27
