Question 88

The sum of a fraction and 3 times its reciprocal is 31/6. What is the fraction?

Solution

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

$$ \frac{1}{x} + 3x = \frac{31}{6}$$

$$\Rightarrow (1+3x^{2}) = \frac{31}{6} \times x$$

$$\Rightarrow 18x^{2}-31x+6 = 0$$

$$\Rightarrow(x-\frac{27}{18})(x-\frac{4}{18})=0$$

$$\Rightarrow(x-\frac{3}{2})(x-\frac{2}{9})=0$$

$$\Rightarrow x = 3/2 or 2/9$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 2/3 \text(or) 9/2$$

so the answer is option B.

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