In a Young's double slit setup, the intensities arriving at a point from the two slits are $I$ and $4I$. The ratio of the maximum to minimum intensity in the resulting fringe pattern is:

Amplitudes scale as the square root of intensity, so $A_1 : A_2 = 1 : 2$. Maximum amplitude $= A_1 + A_2 = 3$ and minimum amplitude $= |A_2 - A_1| = 1$. Intensity ratio $= 3^2 : 1^2 = 9 : 1$.