Question

If the numerator of a fraction is increased by $200$ percent and the denominator is increased by $350$ percent, the resultant fraction is $\frac{5}{12}$. What will be its original fraction?

Answer 1

Calculate the fraction

Let the numerator of the fraction be $x$ and the denominator of the fraction be $y$, then the fraction will be $\frac{x}{y}$.

According to question:-

The numerator is increased by $200\%$ so that the numerator becomes :

$\left[x+\frac{200\times x}{100}\right]=3x$ $---------------\left(1\right)$

and , the denominator is increased by $350\%$ so that the denominator becomes:

$\left[y+\frac{350\times y}{100}\right]=\frac{45y}{10}$ $---------------\left(2\right)$

Now, the new fraction becomes;

$$\begin{gathered} \frac{3x}{\left({\displaystyle \frac{45y}{10}}\right)}=\frac{5}{12} \\ \Rightarrow \frac{30x}{45y}=\frac{5}{12} \\ \Rightarrow 360x=225y \\ \Rightarrow \frac{x}{y}=\frac{225}{360} \\ \Rightarrow \frac{x}{y}=\frac{5}{8} \end{gathered}$$

Hence, If the numerator of a fraction is increased by $200$ percent and the denominator is increased by $350$ percent, the resultant fraction is $\frac{5}{12}$then its original fraction is $\frac{5}{8}$.