Question 38

Sum of four times a fraction and 7 times its reciprocal is 16. What is the fraction?

Solution

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

$$ 4(\frac{1}{x}) + 7x = 16$$

$$\Rightarrow (4+7x^{2}) = 16 \times x$$

$$\Rightarrow 7x^{2}-16x+4 = 0$$

$$\Rightarrow(x-\frac{14}{7})(x-\frac{2}{7})=0$$

$$\Rightarrow(x-2)(x-\frac{2}{7})=0$$

$$\Rightarrow x = 2 or 2/7$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 1/2 \text(or) 7/2$$

so the answer is option B.

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