Football Passing Data Sufficiency

Let Raju be $A$, Ratan be $B$, and Rivu be $C$. $A$ and $B$ are midpoints of shorter sides of length $w$, so $AB = L$ (the length of the ground). Triangle $ACB$ is right-angled at $C$. Since $C$ lies on a longer side, the perpendicular distance from $C$ to $AB$ is $w/2$. Using Statement I: $L = 80$, $w = 50$. $AB = 80$. In right triangle $ACB$, $AC^2 + BC^2 = AB^2 = 80^2 = 6400$. Area of $\Delta ACB = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 80 \times 25 = 1000$. Also, Area $= \frac{1}{2} x y = 1000 \implies xy = 2000$. $(x+y)^2 = x^2 + y^2 + 2xy = 6400 + 4000 = 10400 \implies x+y = 20\sqrt{26}$. Total distance traveled by the ball $= x + y + 80 = 20\sqrt{26} + 80$. Time taken $= \frac{x+y+80}{10} + 3 + 2$, which can be uniquely determined. Thus, Statement I alone is sufficient. Statement II alone gives area = 1000, which gives $xy = 2000$, but without knowing $AB$ (or $x^2 + y^2$), we cannot find $x+y+AB$. Hence, Statement I alone is sufficient.