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