The difference between the boiling point and freezing point of an aqueous solution containing sucrose (molecular mass = $342 g$ $mol^{-1}$) in $100\,g$ of water is $105 .0^\circ C$. If $K_f \,and\, K_b$ of water are $1.86$ and $0.51 \,K \,kg mol^{-1}$ respectively, the weight of sucrose in the solution is about