Question

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers the ratio is 4 : 5. Find the numbers

Answer 1

Let the two numbers be $x$ and $y$.
According to the question, $\frac{x}{y}=\frac{5}{6}$
$\Rightarrow y=\frac{6x}{s}\dots \left(i\right)$
$Also,\frac{x-8}{y-8}=\frac{4}{5}$
$\Rightarrow 5(x-8)=4(y-8)$
$\Rightarrow 5x-40=4y-32$
$\Rightarrow 5^{x-4y}=8\dots \left(\text{ii}\right)$
On putting the value of $y=\frac{6x}{5}$ in Eq. (ii), we get
$5x-4\left(\frac{6x}{5}\right)=8$
$\Rightarrow \frac{25x-24x}{5}=8$
$\Rightarrow x=40$
On putting the value of $x=40$ in Eq. (i), we get
$y=\frac{6\times 40}{5}=48$
Hence, the two numbers are 40 and 48 .