Two coherent sources $S_1$ and $S_2$ are separated by a distance four times the wavelength l of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is 

 

From  $\Delta S_1{S}_{2}D,$
${\left(S_{1}D\right)}^2={\left(S_1{S}_2\right)}^2+{\left(S_{2}D\right)}^2$
${(S_{1}P+PD)}^2={\left(S_1{S}_2\right)}^2+{\left(S_{2}D\right)}^2$

Here $S_{1}P$  is the path difference $=n\lambda$  for maximum intensity. 
$\therefore {(n\lambda +x_n)}^2={\left(4\lambda \right)}^2+{\left(x_n\right)}^2$
or  $x_n=\frac{16{\lambda }^2-n^2{\lambda }^2}{2n\lambda }$
Then  $x_1=\frac{16{\lambda }^2-{\lambda }^2}{2\lambda }=7.5\lambda$
$x_2=\frac{16{\lambda }^2-4{\lambda }^2}{4\lambda }=3\lambda$
$x_3=\frac{16{\lambda }^2-9{\lambda }^2}{6\lambda }=\frac{7}{6}\lambda$
$x_4=0$.
$\therefore$Number of points for maxima becomes 3.