Question

If the ratio of HM and GM of two quantities is $12:13$, then the ratio of the number is ?

• A. $1:2$
• B. $2:3$
• C. $3:4$
• D. None of these

Answer 1

The correct option is D None of these

Let the numbers be $a$ and $b$ then,

$HM=\frac{2ab}{(a+b)}andGM=\sqrt{ab}A/Q,\frac{HM}{GM}=\frac{2ab}{(a+B)\sqrt{ab}}=\frac{12}{13}\Rightarrow \frac{\sqrt{ab}}{a+b}=\frac{6}{13}\Rightarrow \frac{a+b}{\sqrt{ab}}=\frac{13}{6}\Rightarrow \sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}=\frac{13}{6}Let\sqrt{\frac{a}{b}}=x\therefore x+\frac{1}{x}=\frac{13}{6}\Rightarrow 6x^2-13x+6=0\Rightarrow x=\frac{2}{3}or\frac{3}{2}\therefore x^2=\frac{a}{b}\Rightarrow \frac{a}{b}=\frac{4}{9}or\frac{9}{4}$