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

Find the number

Let the numerator be $x$

then, the denominator$=2x-2$

Adding $3$ in both numerator and denominator, we get,

$\Rightarrow \frac{x+3}{2x-2+3}=\frac{2}{3}$

$\Rightarrow 3x+9=4x+2$

$\Rightarrow x=7$

Now, numerator $=7$ and denominator $=2\left(7\right)-2=12$

Hence, the original number is $\frac{7}{12}$.