Question 88

A fraction is greater than its reciprocal by 9/20. What is the fraction?

Solution

Let that fraction be $$\frac{1}{x}$$

$$ (\frac{1}{x}) = x + 9/20$$

$$\Rightarrow 20x^{2}+9x-20 = 0$$

$$\Rightarrow(x+\frac{25}{20})(x-\frac{16}{20})=0$$

$$\Rightarrow(x+5/4)(x-4/5)=0$$

$$\Rightarrow x = -5/4 or 4/5$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = -4/5 \text(or) 5/4$$

so the answer is option A.

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