Question

Two numbers are in ratio $4:5$. The difference of their squares is $81$. Find the numbers.

Answer 1

Let one number is $x$ another is $y$

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

$y=\frac{5x}{4}$ ……$\left(1\right)$

Differentiate of square$=y^2-x^2=81$

${\left(\frac{5x}{4}\right)}^2-x^2=81$

$\frac{9}{16}{x}^2=81$

$x^2=9\times 16$

$x=12$

$y=15$.