Question

If the numerator of a fraction is increased by 25% and the denominator is increased by 10%,it becomes 2/5.find the original fraction

Answer 1

Answer:

The original fraction is 44/125

Step-by-step explanation:

$\text{Let the fraction be }\frac{x}{y}$

when the numerator is increased by 25%,

$\text{Numerator =}$

$=x+\frac{25}{100}*x$

$=x+\frac{x}{4}$

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

when the denominator is increased by 10%

$\text{Denominator =}$

$=y+\frac{10}{100}*y$

$=y+\frac{y}{10}$

$=\frac{11y}{10}$

As per given data,

$\frac{\frac{5x}{4}}{\frac{11y}{10}}=\frac{2}{5}$

$\implies\frac{5x}{4}*\frac{10}{11y}=\frac{2}{5}$

$\implies\frac{50x}{44y}=\frac{2}{5}$

$\implies\frac{25x}{22y}=\frac{2}{5}$

$\implies\boxed{\bf\frac{x}{y}=\frac{44}{125}}$