As we know, resultant intensity is given by,

$I=4I_0 {\cos }^2\left(\frac{\Delta \varphi }{2}\right)$ and phase difference can be written as $∆\varphi =\frac{2\pi }{\lambda }∆x$.

For first case:

$I_{\mathit{1}}=4I_0 {\cos }^2\left(\frac{2\pi }{\lambda }\times \frac{\lambda }{4}\right)=4I_0 {\cos }^2\left(\frac{\pi }{4}\right)=2I_{\mathit{0}}$

For second case:

$I_{\mathit{2}}=4I_0 {\cos }^2\left(\frac{2\pi }{\lambda }\times \frac{\lambda }{3}\right)=4I_0 {\cos }^2\left(\frac{2\pi }{3}\right)=I_{\mathit{0}}$

Therefore, required value of$\frac{I_1+I_2}{I_0}=3$.