When a hole is made at depth y below the liquid surface, the efflux velocity is given by Torricelli's theorem: $v=\sqrt{2gy}$. The time for the liquid to fall the remaining height (H - y) to the ground is $t=\sqrt{\frac{2(H-y)}{g}}$. The horizontal range is x = v × t.

Combining these, we get $x=2\sqrt{y(H-y)}$. This is an equation for x in terms of y. To find its maximum value, we can treat it as a function of y. The expression y(H - y) is maximized when y = H/2, following the property of a downward parabola. Therefore, x is maximum when y = H/2, and the maximum value is $x_{\max }=H$. This maximum range is independent of the liquid's density and the acceleration due to gravity (g).

Final Answer: x is maximum for y = H/2