Question

The harmonic mean between two numbers is $14\frac{2}{3}$ and geometric mean is $24$. The greater number between them is

• A. 72
• B. 54
• C. 36
• D. none of these

Answer 1

The correct option is D none of these

Let the two numbers be x, y

Given, $\frac{2xy}{x+y}=\frac{44}{3}$ and $\sqrt{xy}=24$

$\Rightarrow xy=576$

$\Rightarrow 2xy=\frac{44}{3}(x+y)$

$\Rightarrow 576\times 3=22(x+y)$

$\Rightarrow x+y=\frac{864}{11}$

(A) if $x=72$

$\Rightarrow y=576/72=8$

But $x+y\ne 864/11$

(B) $x=54$

$\Rightarrow y=576/54$

$\Rightarrow x+y=54+\frac{576}{54}\cong 64\ne \frac{864}{11}$

$(\sim 78)$

(C) $x=36$

$\Rightarrow y=16$

$\Rightarrow x+y=52\ne \frac{864}{11}$.