Two persons $A$ and $B$ perform same amount of work in moving a body through a certain distance $d$ with application of forces acting at angles $45^{\circ}$ and $60^{\circ}$ with the direction of displacement respectively. The ratio of force applied by person $A$ to the force applied by person $B$ is $\frac{1}{\sqrt{x}}$. The value of $x$ is $\_\_\_\_$.