Question

Let a, b be two positive numbers, where a>b and $4\times GM=5\times HM$ for the numbers. Then a is

• A. 4b
• B. $\frac{1}{4}b$
• C. 2b
• D. b

Answer 1

The correct option is A 4b

Given
$4\sqrt{ab}=5\times \frac{2ab}{a+b}$
$\Rightarrow (a+b)=\frac{5\sqrt{ab}}{2}$_________(1)
$\Rightarrow a^2+b^2+2ab=\frac{25ab}{4}$
$\Rightarrow (a+b)=\frac{5}{2}\sqrt{ab}$
$\Rightarrow a^2+b^2-2ab=\frac{9ab}{4}$
$\Rightarrow a-b=\frac{3\sqrt{ab}}{2}(\because a>b)$______(2)
$\therefore 2a=4\sqrt{ab}$ from (1) and (2)
$\Rightarrow a=4b$