[tex]\{a,b,c\} i.p.\{2,5,6\}\Rightarrow \dfrac{a}{\frac{1}{2}}=\dfrac{b}{\frac{1}{5}}=\dfrac{c}{\frac{1}{6}}=k\Rightarrow a=\dfrac{k}{2},b=\dfrac{k}{5},c=\dfrac{k}{6}\\
a-b=15\\
\dfrac{k}{2}-\dfrac{k}{5}=15|\cdot 10\\
5k-2k=150\\
3k=150\Rightarrow \boxed{k=50}\\
a=\dfrac{k}{2}\Rightarrow \boxed{a=25}\\
b=\dfrac{k}{5}\Rightarrow \boxed{b=10}\\
c=\dfrac{k}{6}\Rightarrow \boxed{c=\dfrac{25}{3}}[/tex]