Question

The numerator of a fraction is 2 less than the denominator. If 1 is added to both the numerator and denominator, then it becomes $\frac{3}{5}.$ Find the fraction.

• A. $\frac{4}{2}$
• B. $\frac{6}{4}$
• C. $\frac{2}{4}$
• D. $\frac{4}{6}$

Answer 1

The correct option is C $\frac{2}{4}$

Let the denominator of the number is $y$. So, the numerator is $y-2$.

The fraction is then $\frac{y-2}{y}$. If 1 is added to both the numerator and the denominator, it becomes
$\frac{y-2+1}{y+1}$, which is equal to $\frac{3}{5}$.
$\Rightarrow \frac{y-2+1}{y+1}=\frac{3}{5}\Rightarrow \frac{y-1}{y+1}=\frac{3}{5}$
On cross multiplication, we have
$\Rightarrow 5(y-1)=3(y+1)\Rightarrow 5y-5=3y+3\Rightarrow 2y=5+3\Rightarrow y=\frac{8}{2}\Rightarrow y=4$

Hence, the fraction is $\frac{4-2}{4}=\frac{2}{4}$.