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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
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B
150 hours
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C
100 hours
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D
200 hours
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Solution

The correct option is D $$100$$ 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.

Mathematics

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