Question 88

Sum of four times a fraction and 6 times its reciprocal is 11. What is the fraction?

Solution

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

$$4 \times \frac{1}{x} + 6x = 11$$

$$\Rightarrow (4+6x^{2}) = 11 \times x$$

$$\Rightarrow 6x^{2}-11x+4 = 0$$

$$\Rightarrow(x-\frac{8}{6})(x-\frac{3}{6})=0$$

$$\Rightarrow x = 4/3 or 1/2$$

$$\Rightarrow \text{fraction} = \frac{1}{x} = 3/4 \text(or) 2$$

so the answer is option A.

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