A) p: (q + r)
B) (p + q): r
C) 2: 3
D) 1: 2
Correct Answer: D
Solution :
\[\because \] \[a:b=c:d=e:f=1:2\] \[\Rightarrow \] \[a=\frac{1}{2}b,\] \[c=\frac{1}{2}d,\] \[e=\frac{1}{2}f\] \[\therefore \] \[\frac{pq+qc+re}{pq+qd+rf}=\frac{\begin{matrix} 1 \\ 2 \\ \end{matrix}pb+\begin{matrix} 1 \\ 2 \\ \end{matrix}qd+\begin{matrix} 1 \\ 2 \\ \end{matrix}rf}{pq+qd+rf}\] \[=\frac{1}{2}\left( \frac{pq+qd+rf}{pq+qd+rf} \right)=\frac{1}{2}=1:2\]
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