Question

The ratio of HM and GM for two positive numbers is 4 : 5. What is the ratio of the numbers?

• A. 4 : 1
• B. 3 : 2
• C. 3 : 4
• D. 2 : 3

Answer 1

The correct option is A 4 : 1

$HM=\frac{2ab}{a+b},GM=\sqrt{ab}$
Let two numbers be 4x and 5x
$\frac{HM}{GM}=\frac{4x}{5x}\frac{HM}{GM}=\frac{4}{5}\frac{2ab}{(a+b)}\times \frac{1}{\sqrt{ab}}=\frac{4}{5},$
$\frac{2\sqrt{ab}}{a+b}=\frac{4}{5}$
Therefore, a : b = 4 : 1