Subject
Quantitative Aptitude
Topic
Time and Work
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?
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?
ক)
2 min.খ)
1.5 min.গ)
1 min.ঘ)
30 secঙ)
None of theseExplanation
Quantity of water flowing through 5 cm pipe alone α 5 2 ⇒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 = 3 2 : 4 2 : 5 2 = 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.Related questions
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