Question

Let $\alpha$ and $\beta$ be two numbers where $\alpha <\beta$. The geometric mean of these numbers exceeds the smaller number $\alpha$ by $12$ and the arithmetic mean of the same number is smaller by $24$ than the larger number $\beta$ , then the value of $|\beta -\alpha |$ is :

• A. $27$
• B. $48$
• C. $45$
• D. 44

Answer 1

The correct option is B $48$

$\sqrt{\alpha \beta }=\alpha +12$

and $\frac{\alpha +\beta }{2}+24=\beta$
$\Rightarrow \alpha +\beta +48=2\beta \Rightarrow \beta -\alpha =48\Rightarrow |\beta -\alpha |=48$