In YDSE, if  the sources are incoherent the  intensity on the screen  is 13 $I_o$  when these sources are coherent the minimum intensity on the screen is $I_o$ .if maximum intensity produced by these  coherent  sources on the screen is  $n{I}_0$. Find n 

Given that, in YDSE , if the sources are incoherent , the intensity on the screen is  $13I_0$
When these sources are coherent, the minimum intensity on the screen is  $I_o$. if the maximum intensity produced by these coherent sources on the screen is  $n{I}_0$, we have to find n 
For incoherent sources ,we just add the interfering intensities to get the resultant intensity.
So,  $I_1+I_2=13I_{\mathrm{0..........}\left(i\right)}$
Also, for coherent sources, the minimum intensity is  
$$\begin{gathered} {(\sqrt{I_1}-\sqrt{I_2})}^2=I_0 \\ \Rightarrow I_1+I_2-2\sqrt{I_1}\sqrt{I_2}=I_0 \end{gathered}$$
 $\Rightarrow 13I_0-2\sqrt{I_1}\sqrt{I_2}=I_0$  (from(i))
$2\sqrt{I_1}\sqrt{I_2}=12I_0\mathrm{.........}\left(ii\right)$
For coherent sources, the maximum intensity is  $I_{\max }=I_1+I_2+2\sqrt{I_1}\sqrt{I_2}$
$\Rightarrow I_{\max }=13I_0+12I_0=25I_0$  from (i) and (ii) )