If a : b = c : d, then $$\frac{{{\text{ma}} + {\text{nc}}}}{{{\text{mb}} + {\text{nd}}}}$$   is equal to -

$$\eqalign{ & {\text{Let }}\frac{a}{b} = \frac{c}{d} = k \cr & {\text{Then,}} \cr & \Rightarrow a = bk,\,c = dk \cr & \therefore \frac{{ma + nc}}{{mb + nd}} \cr & = \frac{{mbk + ndk}}{{mb + nd}} \cr & = \frac{{k\left( {mb + nd} \right)}}{{\left( {mb + nd} \right)}} \cr & \Rightarrow k = \frac{a}{b} \cr & \Rightarrow a:b \cr} $$