Question

If two numbers $a,b$ are such that $a:b=8:3$ and $a-5:b+6=5:3$, then $a-7:b+7$ is equal to

• A. $\frac{6}{7}$
• B. $\frac{5}{4}$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is D $\frac{3}{2}$

Here, $\frac{a}{b}=\frac{8}{3}$
$\Rightarrow \frac{a}{8}=\frac{b}{3}=n\left(\text{say}\right)$
So, $a=8n,b=3n$

$\frac{a-5}{b+6}=\frac{5}{3}$
$\Rightarrow \frac{8n-5}{3n+6}=\frac{5}{3}$
$\Rightarrow n=5$
$\Rightarrow a=40,b=15$

$\therefore \frac{a-7}{b+7}=\frac{33}{22}=\frac{3}{2}$