Two waves of intensity ratio 1: 9 cross each other at a point. The...

For incoherent wave, ${I}_{1} = {I}_{A} + {I}_{B} ⇒ {I}_{1} = {I}_{0} + 9{I}_{0}$

^{$⇒ {I}_{1} = 10{I}_{0}$}

For coherent wave ${I}_{2} = {I}_{A} + {I}_{B} + 2\sqrt{{I}_{A}{I}_{B}}cos{60}^{o}$

$⇒ {I}_{2} = {I}_{0} + 9{I}_{0} + 2\sqrt{9I 02} \times \dfrac{1}{2} = 13{I}_{0}$

$⇒ \dfrac{{I}_{1}}{{I}_{2}} = \dfrac{10}{13}$

Therefore, $x = 13$.