A) 1 : 3
B) 1 : 2
C) 2 : 3
D) 2 : 1
Correct Answer: C
Solution :
\[\frac{p}{q}=\frac{r}{s}=\frac{t}{u}=\frac{2}{3}\] Let\[\frac{p}{q}=\frac{2}{3}=\frac{2{{K}_{1}}}{3{{K}_{1}}};\frac{r}{s}=\frac{2{{K}_{2}}}{3{{K}_{1}}};\frac{r}{s}=\frac{2{{K}_{2}}}{3{{K}_{2}}};\frac{t}{u}=\frac{2{{K}_{3}}}{3{{K}_{3}}}\] \[\therefore p=2{{K}_{1}};r=2{{K}_{2}};t=2{{K}_{3}}\] and\[q=3{{K}_{1}};s=3{{K}_{2}};u=3{{K}_{3}}\] \[\therefore \] \[(mp+nr+ot):(mq+ns+ou)\] \[=(m\times 2{{K}_{1}}+n\times 2{{K}_{2}}+o\times 2{{K}_{3}}):\]\[(m\times 3{{K}_{1}}+n\times 3{{K}_{2}}+o\times 3{{K}_{3}})\] \[=(m{{K}_{1}}+n{{K}_{2}}+o{{K}_{3}});\]\[(m{{K}_{1}}+n{{K}_{2}}+o{{K}_{3}})\] \[=2:3\]
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