The rate at which water flows through a pipe is proportional to the square of the diameter of the pipe. A pipe of diameter 3 cm alone fills an empty tank in 32 minutes. How long will a pipe of diameter 4 cm alone take to fill the same empty tank?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 18 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 4 cm pipe : rate of 3 cm pipe \(=4^2:3^2=16:9\)
Time of 4 cm pipe : time of 3 cm pipe \(=9:16\)
Time of 4 cm pipe \(\displaystyle =32\times\frac{9}{16}=18\) minutes
The 4 cm pipe fills the tank in 18 minutes.