Question

The denominator of a fraction is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 added to the denominator, the value of the fraction becomes $\frac{1}{5}$. Find the original fraction.

Answer 1

Let the numerator be x; so denominator = x + 3
The fraction obtained by subtracting 3 from the numerator and adding 2 to the denominator is 1 : 5.
$\frac{x-3}{x+5}=\frac{1}{5}$
⇒ 5(x − 3) = x + 5
⇒ 5x − 15 = x + 5
⇒ 4x = 20
∴ x = 5
∴ The numerator is 5 and the denominator is 5 + 3 = 8 .
∴ The original fraction is $\frac{5}{8}$