Question

If the numerator of a fraction is increased by $300\%$ and the denominator is increased by $500\%$, the resultant fraction is $\frac{5}{12}$. What was the original fraction?

• A. $\frac{8}{5}$
• B. $\frac{5}{8}$
• C. $\frac{12}{5}$
• D. $\frac{5}{7}$

Answer 1

Answer: (B)

$\frac{5}{8}$

Let the original fraction be $\frac{p}{q}$.

Then, $\frac{p+\frac{300}{100}P}{q+\frac{500}{100}P}=\frac{5}{12}$

$\Rightarrow \frac{4p}{6q}=\frac{5}{12}$
$\Rightarrow \frac{p}{q}=\frac{5}{12}\times \frac{6}{4}=\frac{5}{8}$