Question : A fraction is greater than its reciprocal by $\frac{9}{20}$. What is the fraction?
Option 1: $\frac{5}{4}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{3}$
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Correct Answer: $\frac{5}{4}$
Solution : Let the fraction be $x$. According to the question, $x-\frac{1}{x}=\frac{9}{20}$ $\Rightarrow 20x^2-9x-20=0$ $\Rightarrow 20x^2-25x + 16x-20=0$ $\Rightarrow 5x (4x-5) + 4x (4x-5)=0$ $\Rightarrow (4x-5) (5x+4)=0$ $\Rightarrow (4x-5) =0$ or $ (5x+4)=0$ $\therefore x=\frac{-4}{5},\frac{5}{4}$ Hence, the correct answer is $\frac{5}{4}$.
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