Question 88

The sum of a fraction and 10 times its reciprocal is 37/4. What is the fraction?

Solution

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

$$ (\frac{1}{x}) + 10x = 37/4$$

$$\Rightarrow (4+40x^{2}) = 37 \times x$$

$$\Rightarrow 40x^{2}-37x+4 = 0$$

$$\Rightarrow(x-\frac{5}{40})(x-\frac{32}{40})=0$$

$$\Rightarrow(x-1/8)(x-\frac{4}{5})=0$$

$$\Rightarrow x = 1/8 or 4/5$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 8 \text(or) 5/4$$

so the answer is option A.

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