The denominator of a fraction is $$4$$ more than twice its numerator. Denominator becomes $$12$$ times the numerator, if both the numerator and the denominator are reduced by $$6$$, find the fraction.
Let the numerator be $$x$$
$$\therefore$$ denominator $$= 2x + 4$$
According to equation
$$12 (x - 6) = 2x + 4 - 6$$
$$12x - 72 = 2x - 2$$
$$12 - 2x = 72 - 2$$
$$10x = 70$$
$$x = \dfrac{70}{10}$$
$$x = 7$$
Numerator $$= 7$$
Denominator $$= 2(7) + 4 = 14 + 4$$
$$= 18$$
Fraction $$= \dfrac{numerator}{denominator} = \dfrac{7}{18}$$