The quantity of water which flows through a pipe is proportional to the square of its diameter. If a pipe of 5 cm diameter can fill a tank in 1min. How long would 3 pipes of 3cm, 4cm and 5cm diameter together take to fill it?
Solution
Correct Answer: Option D
Quantity of water flowing through 5 cm pipe alone α 52
⇒quantity of water flowing through 5 cm pipe in unit time = 25k
Where, k is the constant of proportionality
The quantity of water equal to 25k fills the tank completely in 1 min.
Now, 3 pipes are given of diameter 3 cm, 4 cm and 5 cm respectively
The quantity of water which flows through a pipe is proportional to the square of its diameter.
∴ Ratio of water flowing through the 3 pipes respectively = 32 : 42 : 52= 9 : 16 : 25
⇒quantity of water flowing through 3 cm pipe in unit time = 9k
⇒quantity of water flowing through 4 cm pipe in unit time = 16k
⇒quantity of water flowing through 5 cm pipe in unit time = 25k
⇒quantity of water flowing through all three pipes in unit time = 9k + 16k + 25k = 50k
Now, twice of the previous amount is being poured in the tank.
∴time taken = half of previous time
∴time taken = ½ min = 30 sec.
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