Q. The HM of two numbers is 4. Their AM is $A$ and GM is $G$. If $2A + G^{2} = 27$, then $A$ is equal to
A) 9
B) $\frac{9}{2}$
C) 18
D) 27
Explanation
(b)
Let the two numbers be $a$ and $b$
Since, $\frac{2ab}{a + b} = 4,\ \ \ A = \frac{a + b}{2}$
and $G = \sqrt{ab}$
$\therefore\ \frac{2ab}{2A} = 4\ \Rightarrow A = \frac{ab}{4}$
and $G^{2} = 4A$
Given, $2A + G^{2} = 27$
$\therefore\ 2A + 4A = 27$
$\Rightarrow \ A = \frac{9}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.