Question

The ratio of two number is $8:7$ .If $2$ subtracted from both the number, the ratio changes to $7:6$. Find the numbers.

Answer 1

Let $x$ and $y$ be the required numbers such that

$\frac{x}{y}=\frac{8}{7}$

$\Rightarrow x=\frac{8}{7}y.....\left(1\right)$

Also, given that,

$\frac{x-2}{y-2}=\frac{7}{6}$

$6(x-2)=7(y-2)$

$\Rightarrow 6x-12=7y-14$

$\Rightarrow 6\cdot \frac{8}{7}y-7y=12-14$

$\Rightarrow \frac{48}{7}y-7y=-2$

$\Rightarrow \frac{48y-49y}{7}=-2$

$\Rightarrow y=(-2)\times (-7)=14$

Substituting the value of $y$ in equation $\left(1\right)$, we have

$x=\frac{8}{7}\times 14=16$

Hence the required numbers are $16$ and $14$.