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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