\[\begin {array} {1 1} (a)\;54\;seconds \\ (b)\;90\;seconds \\ (c)\;32 \;seconds \\ (d)\;15\;seconds \end {array}\]

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Now we know volume of water flowing out per second from the hole of area a is given by

Volume / second $= a v$

Where v= velocity of e flux

$v= \sqrt {2gh}$

$\therefore $ Time taken to empty water equal to volume of water initially present $t =\large\frac{A \times h}{av}$

$A$ = Area of vessel

$h$ = height of water

$t=\large\frac{A}{a} \sqrt{\frac {h}{2g}}$

$\quad= 100 \sqrt {\large\frac{2}{2 \times 9.8}}$

$\quad=\large\frac{100}{\sqrt {9.8}}$

$\quad \approx 32\;seconds$

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