If a : b = c : d, then ma + nc mb + nd is equal to -

Answer: Option D

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