Question

Two numbers are in the ratio $3:4$. If $4$ is added to each, the ratio becomes $4:5$. Find the numbers.

Answer 1

Let the two numbers be $x$ and $y$.
As per condition 1, i.e., Two numbers are in the ratio 3 : 4.
The equation becomes,
$\frac{x}{y}=\frac{3}{4}$
$\therefore 4x-3y=0$ ..........(1)
As per condition 2, If $4$ is added to each, the ratio becomes $4:5$.
The equation becomes,
$\frac{x+4}{y+4}=\frac{4}{5}$
$\therefore 5x-4y=-4$ ...........(2)
Equation (1) can be written as $x=\frac{3y}{4}$
Substituting $x=\frac{3y}{4}$ in (2) we get,
$y=16$
Re substituting $y=16$ in (1) we get,
$x=12$
Hence Numbers are $12$ and $16$