Question

If the A.M. of two numbers is greater than G.M. of the numbers by 2 and the ratio of the numbers is 4, then the numbers are

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

Answer 1

The correct option is D None of these

Suppose that required numbers are a and b.
Now $A.M.=\frac{a+b}{2}$ and $G.M.=\sqrt{ab}$
Under conditions,
$A.M.=G.M.+2\Rightarrow \frac{a+b}{2}=\sqrt{ab}+2$ ....(i)
and $\frac{a}{b}=\frac{4}{1}\Rightarrow a=4b$ ....(ii)
From (ii) and (i), we get a = 16 and b = 4.