Question

The denominator of a rational number is greater then its numerator by $4$. If the numerator is increased by $11$ and the denominator is decreased by $1$, the new number becomes $7/3$. Find the original.

Answer 1

let the numerator = $x$

So, denominator=-$x+4$

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

According to question,

$\frac{x+11}{x+4-1}=\frac{7}{3}$

$⟹3(x+11)=7(x+3)$

$⟹4x=12$

$⟹x=3$

Hence, original number $=\frac{3}{7}$