Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi}{2}$ at point A and $\pi$ at point B. Then the difference between the resultant intensities at A and B is

4I

At point A, resultant intensity

$I_A=I_1+I_2=5 I$; and at point B

$ I_B=I_1+I_2+2 \sqrt{I_1~I_2} \cos \pi=5 I+4 I$

$I_B=9 I$  so  $I_B-I_A=4 I$.