Question

A certain fraction is equivalent to $\frac{1}{2}$. If $3$ is added to its numerator and $2$ is added to its denominator, the resulting fraction is equivalent to $\frac{3}{4}$. What is the numerator of the original fraction?

• A. $2$
• B. $3$
• C. $4$
• D. $5$
• E. $6$

Answer 1

The correct option is B $3$

Let the fraction be $\frac{x}{y}$ which is equivalent to $\frac{1}{2}$.

So, we get $2x=y$.

Now $3$ is added to numerator and $2$ is added to denominator.

We get $\frac{(x+3)}{(y+2)}$ $=\frac{3}{4}$.

$\therefore 4x+12=3y+6$

$\therefore 4x+6=3y$

Substitute $2x=y$ in the equation,

$2y+6=3y$

$\Rightarrow y=6$

Now, $x=\frac{y}{2}=\frac{6}{2}=3$

Therefore, the numerator of original fraction is $x=3$.