Question

The ratio of two numbers is $7:6$. If $3$ is added to the greater number and $2$ is subtracted from smaller number then the new ratio comes to be $3:2$, then the numbers are

• A. $7$ and $6$
• B. $14$ and $12$
• C. $21$ and $18$
• D. $28$ and $14$

Answer 1

The correct option is C $21$ and $18$

Let the numbers be $a,b$
$\frac{a}{b}=\frac{7}{6}$
$\Rightarrow a=7n,b=6n$
Now, $\frac{a+3}{b-2}=\frac{3}{2}$
$\Rightarrow \frac{7n+3}{6n-2}=\frac{3}{2}$
$\Rightarrow n=3$
$\therefore a=21,b=18$