A) 1 : 2 : 3
B) 3 : 2 : 1
C) 4 : 2 : 3
D) 2 : 4 : 7
Correct Answer: A
Solution :
\[\frac{y}{x-z}=\frac{y+x}{z}\] \[\Rightarrow \] \[yz=xy+{{x}^{2}}-xz-yz\] ?(i) Also, \[\frac{x}{y}=\frac{y}{x-z}\] \[\Rightarrow \] \[{{x}^{2}}-xz={{y}^{2}}\] ?(ii) From Eqs. (i) and (ii), we get \[yz=xy-yz+{{y}^{2}}\] \[\Rightarrow \] \[2yz=xy+{{y}^{2}}\] \[\therefore \] \[yz=x+y\] ?(iii) Hence, only option (c) statistics the Eq. (iii).
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