\(\frac{{{I_{\max }}}}{{{I_{\min }}}} = \frac{{{{\left( {\sqrt {\frac{{{\omega _1}}}{{{\omega _2}}} + 1} } \right)}^2}}}{{{{\left( {\sqrt {\frac{{{\omega _1}}}{{{\omega _2}}} - 1} } \right)}^2}}}\)

\(I_{\max }\) and \(I_{\min }\) are maximum and minium intensity

\(\omega_{1}\) and \(\omega_{2}\) are widths of two slits

\(\therefore \,\,\frac{{{I_{\max }}}}{{{I_{\min }}}} = \frac{{{{\left( {\sqrt {\frac{1}{{25}}}  + 1} \right)}^2}}}{{{{\left( {\sqrt {\frac{1}{{25}}}  - 1} \right)}^2}}}\) \(\left( {\frac{{{\omega _1}}}{{{\omega _2}}} = \frac{1}{{25}}\operatorname{given} } \right)\)

On solving we get,

\(\frac{{{I_{\max }}}}{{{I_{\min }}}} = \frac{{\frac{{36}}{{25}}}}{{\frac{{16}}{{25}}}} = \frac{9}{4} = 9:4\)