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The level of water in a vessel falls from a height 36 cm to 16 cm in 6 minutes as water flows out through a hole in its bottom. At the end of next 3 minutes, the height of water level in the vessel will be

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6 cm

3 cm

9 cm

2 cm

answer is C.

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Detailed Solution

$t \propto \sqrt{h_{1}} - \sqrt{h_{2}}$

$\frac{6}{3} = \frac{\sqrt{36} - \sqrt{16}}{\sqrt{16} - \sqrt{h}} = \frac{6 - 4}{4 - \sqrt{h}}$

$2 = \frac{2}{4 - \sqrt{h}} \Rightarrow 4 - \sqrt{h} = 1$

$\Rightarrow \sqrt{h} = 3 \Rightarrow h = 9 c m$

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