Question

The harmonic mean of two numbers is $ 4 $ and the arithmetic and geometric mean satisfy the relation $ 2\, A + G^2 =27 $ , the numbers are

• A. 6 , 3
• B. 5 , 4
• C. 5 , -2.5
• D. -3 , 1

Answer 1

Answer: (A)

Let numbers be $x$ and $y$.
Then, $A=\frac{1}{2}(x+y), \sqrt{x y}=G$ or $G^{2}=x y$
and $\frac{2 x y}{x+y}=4$
$\Rightarrow G^{2}=4 A$
Also, $2 A+G^{2}=2 A+4 A=27 \Rightarrow A=\frac{9}{2}$
So, $x+y=9, x y=18$
Hence. numbers are $6$ and $3$ .