Question

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

• A. $50$ hours
• B. $150$ hours
• C. $100$ hours
• D. $200$ hours

Answer 1

Answer: (C)

$100$ hours

Volume of water discharged through the pipe $=$ Volume increase of the tank

First, consider the pipe.

Volume discharge through pipe $=$ $\text{length}\times \text{breadth}\times \text{speed}\times \text{time}$

Let the time taken to fill the tank to $3$ m depth be $t$.

Volume discharge through pipe, $V=2\times {10}^{-1}\times 1.5\times {10}^{-1}\times 15\times {10}^3\times t$

$\Rightarrow$ $V=450t$ cu. m

Now consider the tank

Depth of the tank $=$ $3$ m

Volume of the tank $V=150\times 100\times 3$ cu. m

$\Rightarrow$ $V=450\times 100$

Therefore, $450t=450\times 100$

$\Rightarrow$ $t=100$ hours

Therefore, option C is correct.