1. Let the two interfering beams have intensities $I_1 : I_2 = 9:4$ So we can write

   \qquad I_2 = 4k$$ for some constant $k$.

2. In interference of two coherent light beams:

   • Maximum intensity is $I_{\max} = (\sqrt{I_1}+\sqrt{I_2})^2$
   • Minimum intensity is $I_{\min} = (\sqrt{I_1}-\sqrt{I_2})^2$

3. Substitute the given values: $\sqrt{I_1} = \sqrt{9k} = 3\sqrt{k}$ $\sqrt{I_2} = \sqrt{4k} = 2\sqrt{k}$

4. Compute maximum intensity: $I_{\max} = (3\sqrt{k}+2\sqrt{k})^2 = (5\sqrt{k})^2 = 25k$

5. Compute minimum intensity: $I_{\min} = (3\sqrt{k}-2\sqrt{k})^2 = (\sqrt{k})^2 = k$

6. Therefore, the ratio of maximum to minimum intensity is $I_{\max}:I_{\min} = 25k : k = 25:1$

7. Checking options:

   • A: $2:3$ ❌
   • B: $16:81$ ❌
   • C: $25:169$ ❌
   • D: $25:1$ ✅

Hence, the correct answer is Option D.