Question

If the numerator and denominator of a fraction are decreased by $30$ it becomes $\frac{1}{2}$. If the original fraction is $\frac{4}{5}$. Find the fraction ?

Answer 1

let numerator be ${}^{\prime }{x}^{\prime }$ and denominator be ${}^{\prime }{y}^{\prime }$

$\frac{x-30}{y-30}=\frac{1}{2}$

$\frac{x}{y}=\frac{4}{5}\Rightarrow x=\frac{4y}{5}$

$\frac{\frac{4y}{5}-30}{y-30}=\frac{1}{2}\Rightarrow \frac{4y-150}{5y-150}=\frac{1}{2}$

$8y-300=5y-150$

$3y=150\Rightarrow y=50$

$x=40$

Fraction $=\frac{40}{50}$