Question

If the G.M. of two non-zero positive numbers is to their A.M. is 12 :13 then numbers are in the ratio

• A. 5 : 8
• B. 4 : 9
• C. 6 : 11
• D. 3 : 8

Answer 1

The correct option is B 4 : 9

$\frac{G.M}{A.M}=\frac{12}{13}\Rightarrow \frac{AM}{GM}=\frac{13}{12}$, So,$m:n=13:12$
Let the numbers be a and b
Then, $\frac{a}{b}=\frac{m-\sqrt{m^2-n^2}}{m+\sqrt{m^2-n^2}}$
$=\frac{13-\sqrt{169-144}}{13+\sqrt{169-144}}$
$=\frac{13-\sqrt{25}}{13+\sqrt{25}}$
$=\frac{13-5}{13+5}=\frac{8}{18}$
$=\frac{4}{9}=4:9$