Question

The denominator of a fraction is 5 more than its numerator. If the numerator is decreased by 1 and the denominator is increased by 2, the resulting fraction is $\frac{1}{5}$Find the original fraction.

• A. $\frac{9}{4}$
• B. $\frac{3}{4}$
• C. $\frac{3}{8}$
• D. $\frac{-5}{4}$

Answer 1

The correct option is C $\frac{3}{8}$

Let the numerator of the fraction = x
∴ Fraction = $\frac{x}{x+5}$

According to question,
$\frac{x-1}{x+5+2}=15$
⇒$\frac{x-1}{x+7}=15$

By cross multiplication,

⇒
⇒ $5x-5=x+7$
⇒ $4x=12$
⇒ $x=3$

So, the original number = $\frac{x}{x+5}=\frac{3}{8}$