JEE Main 2014 — Laws of Motion Question with Solution

A heavy box is to be dragged along a rough horizontal floor. To do so, the person $A$ pushes it at an angle $30°$ from the horizontal and requires a minimum force $F_{\mathrm{A}}$, while the person $B$ pulls the box at an angle $60°$ from the horizontal and needs minimum force $F_{\mathrm{B}}$. If the coefficient of friction between the box and the floor is $\frac{\sqrt{3}}{5}$, the ratio $\frac{F_{\mathrm{A}}}{F_{\mathrm{B}}}$ is