Question

The ratio between two numbers is $1:3$. If $12$ is added to each number, the ratio between them is $7:15$, then find the original numbers.

Answer 1

Let the numbers be x & y,

$\frac{x}{y}=\frac{1}{3};$ $\frac{x+12}{y+12}=\frac{7}{15}$

$3x=y$

Substituting the value of y in $2^{nd}$ ratio

$\frac{x+12}{3x+12}=\frac{7}{15}$ $\Rightarrow 15x+180=21x+84$

$\Rightarrow 96=6x$

$\Rightarrow x=16$

$y=3x=3\times 16=48$

Numbers $=16,48$.