The rate at which water flows through a pipe is proportional to the square of the diameter of the pipe. A pipe of diameter 2 cm alone fills an empty tank in 45 minutes. How long will a pipe of diameter 3 cm alone take to fill the same empty tank?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 20 minutes
The rate of flow goes as the square of the diameter, and for the same tank the time taken is inversely proportional to the rate.
Rate of 3 cm pipe : rate of 2 cm pipe \(=3^2:2^2=9:4\)
Time of 3 cm pipe : time of 2 cm pipe \(=4:9\)
Time of 3 cm pipe \(\displaystyle =45\times\frac{4}{9}=20\) minutes
The 3 cm pipe fills the tank in 20 minutes.