Question

The denominator of a fraction is greater than the numerator by 5. If 2 is added to both the numerator and the denominator, the value of the fraction so obtained is $\frac{1}{2}$. Find the original fraction.

Answer 1

Let the numerator be x. So, denominator = x + 5.
The fraction obtained by adding 2 to the numerator and denominator is 1: 2.
So, $\frac{x+2}{x+5+2}=\frac{1}{2}$
⇒ 2x + 4 = x + 7
⇒ x = 3
∴ x = 3
∴ the numerator = x = 3
and the denominator = x + 5 = 3 + 5 = 8
∴ the original fraction is $\frac{3}{8}$