A) \[\frac{3}{7}\]
B) \[\frac{7}{3}\]
C) \[\frac{4}{3}\]
D) \[\frac{3}{4}\]
Correct Answer: A
Solution :
Let the fraction be \[\frac{x}{y}\]. According to the question, \[y=2x+1\] ....(1) Also, \[\frac{x}{y}+\frac{y}{x}=2\frac{16}{21}=\frac{58}{21}\] \[\Rightarrow \] \[\frac{x}{2x+1}+\frac{2x+1}{x}=\frac{58}{21}\] (From(1)) \[\Rightarrow \] \[\frac{{{x}^{2}}+4{{x}^{2}}+1+4x}{x(2x+1)}=\frac{58}{21}\] \[\Rightarrow \] \[105{{x}^{2}}+84x+21=116{{x}^{2}}+58x\] \[\Rightarrow \] \[(x-3)\,(11x+7)=0\] \[\Rightarrow \] \[x=3,\] or \[x=-\frac{7}{11}\] (Not possible) \[\therefore \] \[y=7\] \[\therefore \]Required fraction \[=\frac{3}{7}\]
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