Question

In a rational number, twice the numerator is 2 more than the denominator. If 3 is added to each, the numerator and the denominator, the new fraction is 2/3. Find the original number.

Answer 1

Let the denominator be x .
\[ \therefore\text{ The numerator }= \frac{x + 2}{2}\]
\[ \therefore\text{ The rational number }= \frac{x + 2}{2x}\]
According to the question, 
\[\frac{\frac{x + 2}{2} + 3}{x + 3} = \frac{2}{3}\]
\[\text{ or }\frac{x + 2 + 6}{2(x + 3)} = \frac{2}{3}\]
\[\text{ or }\frac{x + 8}{2x + 6} = \frac{2}{3}\]
\[\text{ or }3x + 24 = 4x + 12\]
\[\text{ or }x = 24 - 12\]
\[\text{ or }x = 12\]
\[ \therefore\text{ The rational number }= \frac{12 + 2}{2 \times 12} = \frac{14}{24} = \frac{7}{12}\]