Explanation

(b) Given, $\frac{I_{\max}}{I_{min\ }} = 9 = \frac{\left( a_{1} + a_{2} \right)^{2}}{\left( a_{1} - a_{2} \right)^{2}}$
$\therefore\frac{a_{1} + a_{2}}{a_{1} - a_{2}} = 3$
Or $\ 2a_{1} = 4a_{2}$
Or $\ \ a_{1} = 2a_{2}$
$\Rightarrow \frac{a_{1}}{a_{2}} = 2$
Again, intensity ratio at the screen due to two slits
$\frac{I_{1}}{I_{2}} = \frac{a_{1}^{2}}{a_{2}^{2}} = \frac{4}{1}$
Hence, amplitude ratio is 2 and intensities at the screen due to two slits are 4 units and 1 unit, respectively.