Question

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

Answer 1

Let denominator of the original fraction = x

Then numberator = x - 5

and fraction = $\frac{x-5}{x}$

According to the condition,

$\frac{x-5+3}{x+3}=\frac{4}{5}\Rightarrow \frac{x-2}{x+3}=\frac{4}{5}\Rightarrow 5(x-2)=4x+12\text{(By cross multiplication)}\Rightarrow 5x-10=4x+12\Rightarrow x=22\therefore \text{Original fraction}=\frac{x-5}{x}=\frac{22-5}{22}=\frac{17}{22}$