According to the question

${\mathrm{n}}_1=13, {\mathrm{n}}_2=15, {\mathrm{n}}_3=12, {\mathrm{a}}_1=50, {\mathrm{a}}_2=60, {\mathrm{a}}_3=65$

We know the formula,

Weighted average(Aw)$=\frac{{\mathrm{n}}_1{\mathrm{a}}_1+{\mathrm{n}}_2{\mathrm{a}}_2+{\mathrm{n}}_3{\mathrm{a}}_3}{{\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3}$

Average $=\frac{13\times 50+15\times 60+12\times 65}{13+15+12}$

= ₹ 58.25