Question

If the AM of two numbers is greater than GM of the numbers by $2$ and the ratio of the numbers is $4:1$, then the numbers are

• A. $4,1$
• B. $12,3$
• C. $16,4$
• D. None of these

Answer 1

The correct option is C $16,4$

Let required numbers are $a$ and $b$.
Now, AM $=\frac{a+b}{2}$ and GM $=\sqrt{ab}$
According to the question,
AM $=$ GM $+2$
$\Rightarrow \frac{a+b}{2}=\sqrt{ab}+2$ ...(i)
and $\frac{a}{b}=\frac{4}{1}$
$\Rightarrow a=4b$ ...(ii)
On solving equations (i) and (ii), we get
$a=16,b=4$