# Water flows in a tank 150 m *100 m at the base , through a pipe whose cross - section is 2 dm by 1.5 dm at the speed of 15 km per hour . In what time , will the water be 3 metres deep ?

Solution: Suppose in $x$ hours water will be 3 metres deep in the tank .

Volume of water in the tank $= (150\times 100 \times 3)m^3= 45000m^3$

Area of the cross - section of the pipe   $=$    $\left ( \frac{2}{10}\times \frac{1.5}{10} \right )m^2=(\frac{1}{5}\times \frac{15}{100})m^2=(\frac{3}{100})m^2$

Volume of water that flows in the tank in $x$ hours $=$ (Area of cross section of the pipe ) $\times$  (speed of water )$\times$(time)

$=\frac{3}{100}\times 15000 \times x$    $m^3$                                         [$\because$ speed  = 15km/hr=15000m/hr ]

$=450x$  $m^3$ .

since the volume of water in the tank is equal to the volume of water that flows in the tank in $x$ hours .

$\therefore$            450$x= 45000\Rightarrow x=100$ hours .

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