A water tank which is on ground has an arrangement to maintain a constant water level of depth 60 cm. Through a hole on its vertical wall at a depth of 20cm from the free surface water comes out and reaches  the ground at a certain distance. To have the same horizontal range another hole can be made at a depth of _____________cm

The height of the hole above the ground, y=(H - h), where H is the total depth of the water, if h is the depth of the hole below the water's surface.

Thus the velocity of efflux $\mathrm{v}=\sqrt{2\mathrm{gh}}$  the amount of time it takes a water particle to hit the ground,

$\mathrm{t}=\sqrt{2\mathrm{y}/\mathrm{g}}=\sqrt{\frac{2(\mathrm{H}-\mathrm{h})}{\mathrm{g}}}$

$\mathrm{Range} \mathrm{R}=\mathrm{V}.\mathrm{t}=2\sqrt{\mathrm{h}(\mathrm{H}-\mathrm{h})}$

$2\sqrt{{\mathrm{h}}_1(\mathrm{H}-{\mathrm{h}}_1)}=2\sqrt{{\mathrm{h}}_2(\mathrm{H}-{\mathrm{h}}_2)}$

${\mathrm{h}}_1+{\mathrm{h}}_2=\mathrm{H}$

$\Rightarrow {\mathrm{h}}_2=\mathrm{H}-{\mathrm{h}}_1=(60-20)=40\mathrm{cm}$

Hence the correct answer is 40.