$\begin{array}{1 1} 1:9 \\ 1:4 \\ 3:5 \\ 1:3 \end{array}$

Answer : (a) 1:9

Explanation :$ H=\large\frac{2ab}{a+b}$

$G=\sqrt{a}{b}$

$\frac{H}{G}=\large\frac{2ab/(a+b)}{\sqrt{a}{b}}=\large\frac{3}{5}$

$\large\frac{2\sqrt{a}{b}}{a+b}=\large\frac{3}{5}$

$100\;ab=9(a^2+2ab+b^2)$

$9a^2-82ab+9b^2=0$

$9a^2-81ab-ab+9b^2=0$

$9a(a-9b)-b(a-9b)=0$

$(9a-b)(a-9b)=0$

$9a=b\qquad\;a=9b$

$\frac{a}{b}=1:9\quad\;or\;\quad9:1.$

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