Two light beams of intensities in the ratio of $9:4$ are allowed to interfere. The ratio of the intensity of maxima and minima will be :

Data provided in the question is, the ratio of the intensities,

$\frac{I_1}{I_2}=\frac{9}{4}$

After taking square root of above equation on both sides, we get,

 $\frac{\sqrt{I_1}}{\sqrt{I_2}}=\frac{3}{2}$

Apply componendo and dividendo,
$\Rightarrow \frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}=\frac{3+2}{3-2}=\frac{5}{1}$
$\Rightarrow {\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2=\frac{I_{\max }}{I_{\min }}=\frac{25}{1}$