1. Let the intensities of the two coherent sources be $I_1 : I_2 = 4:1$ So we can take

   \quad I_2=I.$$

2. For interference of two coherent sources, $I_{\max}=(\sqrt{I_1}+\sqrt{I_2})^2$ and $I_{\min}=(\sqrt{I_1}-\sqrt{I_2})^2.$

3. Substitute the given values:

   \quad \sqrt{I_2}=\sqrt{I}.$$ Therefore, $$I_{\max}=(2\sqrt{I}+\sqrt{I})^2=(3\sqrt{I})^2=9I,$$ $$I_{\min}=(2\sqrt{I}-\sqrt{I})^2=(\sqrt{I})^2=I.$$

4. Now compute the required ratio: \frac{I_{\max}+I_{\min}}{I_{\max}-I_{\min}}=rac{9I+I}{9I-I}=rac{10I}{8I}=rac{5}{4}.

5. Given that

   $$$$

\min}}=\frac{5}{x}.$Comparing,$\frac{5}{x}=\frac{5}{4} \implies x=4.$$

6. Hence the correct option is: $\boxed{\text{B: }4}$