A) 1 : 3
B) 1 : 2
C) 2 : 3
D) 3 : 2
Correct Answer: C
Solution :
\[\because \] \[p:q=r:s=t:u=2:3\] \[\Rightarrow \] \[p=\frac{2}{3}q,\] \[r=\frac{2}{3}s,\] \[t=\frac{2u}{3}\] \[\therefore \] \[\frac{mp+nr+ot}{mq+ns+ou}=\frac{\begin{matrix} 2 \\ 3 \\ \end{matrix}mq+\begin{matrix} 2 \\ 3 \\ \end{matrix}ns+\begin{matrix} 2 \\ 3 \\ \end{matrix}ou}{mq+ns+ou}\] \[=\frac{2}{3}\left( \frac{mq+ns+ou}{mq+ns+ou} \right)=\frac{2}{3}=2:3\]
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