b
As, intensity \(I \propto\) width of slit \(W\) Also, intensity \(I \propto\) square of amplitude \(A\)

\(\therefore \quad \frac{I_{1}}{I_{2}}=\frac{W_{1}}{W_{2}}=\frac{A_{1}^{2}}{A_{2}^{2}}\)

But \(\frac{W_{1}}{W_{2}}=\frac{1}{25} \quad\) (given)

\(\therefore \quad \frac{A_{1}^{2}}{A_{2}^{2}}=\frac{1}{25} \quad\) or \(\quad \frac{A_{1}}{A_{2}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)

\(\therefore \,\frac{{{I_{\max }}}}{{{I_{\min }}}} = \frac{{{{\left( {{A_1} + {A_2}} \right)}^2}}}{{{{\left( {{A_1} - {A_2}} \right)}^2}}}\) \( = \frac{{{{\left( {\frac{{{A_1}}}{{{A_2}}} + 1} \right)}^2}}}{{{{\left( {\frac{{{A_1}}}{{{A_2}}} - 1} \right)}^2}}}\)

\( = \frac{{{{\left( {\frac{1}{5} + 1} \right)}^2}}}{{{{\left( {\frac{1}{5} - 1} \right)}^2}}}\) \( = \frac{{{{\left( {\frac{6}{5}} \right)}^2}}}{{{{\left( { - \frac{4}{5}} \right)}^2}}}\) \( = \frac{{36}}{{16}} = \frac{9}{4}\)