Question

Two numbers are in the ratio of $3:4.$ If 8 is added to each number, they become in the ratio of $4:5.$ Find the numbers.

Answer 1

Let the two numbers be $x$ and $y$
According to the question, $\frac{x}{y}=\frac{3}{4}\dots$(i)
$\Rightarrow y=\frac{4x}{3}$
Also, $\frac{x+8}{y+8}=\frac{4}{5}$
$\Rightarrow 5(x+8)=4(y+8)$
$\Rightarrow 5x+40=4y+32$
$\Rightarrow 5x-4y=-8\dots \left(\text{ii}\right)$
On putting the value of $y=\frac{4x}{3}$ in Eq. (ii), we get
$5x-4\left(\frac{4x}{3}\right)=-8$
$\Rightarrow \frac{15x-16x}{3}=-8$
$\Rightarrow x=24$
On putting the value of $x=24$ in Eq. (i), we get
$y=\frac{4\times 24}{3}=32$
Hence, the two numbers are $24$ and $32$ .