Question

The numerator of a fraction is 3 less than its denominator. If the numerator is tripled and the denominator is increased by 2, the value of the fraction obtained is $\frac{1}{2}$. What was the original fraction?

Answer 1

Let the numerator be x; so, denominator = x + 3 .
The ratio of three times the numerator to the denominator’s value increased by two is 1 : 2.
$$\begin{gathered} \mathrm{So},\frac{3x}{x+3+2}=\frac{1}{2} \\ \Rightarrow \frac{3x}{x+5}=\frac{1}{2} \end{gathered}$$
⇒ 6x = x + 5
⇒ x = 1
∴ The numerator is 1 and the denominator is 1+ 3 = 4 .
∴ The original fraction is $\frac{1}{4}$