Question

A tank is $7$ metres long and $4$ metres wide. At what speed should water run through a pipe $5$ cm broad and $4$ cm deep so that in $6$ hours and $18$ minutes, water level in the tank rises by $4.5$ metres?

• A. $10$ km/hr
• B. $12$ km/hr
• C. $8$ km/hr
• D. $18$ km/hr

Answer 1

The correct option is A $10$ km/hr

Let the flow of water be $x$ cm/minute.
$\therefore$ Volume of water that flowed in the tank in $1$ minute $=5\times 4\times x=20x{\text{cm}}^3$
$\therefore$ Volume of water that flowed in the tank in $6$ hours $18$ minutes i.e., $(6\times 60+18)=378$ minutes
$=20x\times 378{\text{cm}}^3\cdot \text{minute}$

According to question,
$20x\times 378=700\times 400\times 450$
$\Rightarrow x=\left(\frac{700\times 400\times 450}{20\times 378}\right)\text{cm/minute}$
$=\left(\frac{700\times 400\times 450\times 60}{20\times 378\times 100000}\right)\text{km/hr}$
$=10\text{km/hr}$