Two pipes A and B fill a tank in 15 and 30 minutes respectively. A third pipe…
2017
Two pipes A and B fill a tank in 15 and 30 minutes respectively. A third pipe C empties it in 20 minutes. If all the three pipes are opened simultaneously, then the time taken to fill the tank will be:
- A.
45 minutes
- B.
35 minutes
- C.
20 minutes
- D.
10 minutes
Attempted by 17 students.
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Correct answer: C
Step-by-Step Solution
To solve this problem, we calculate the net rate of the pipes by considering the filling pipes as positive and the emptying pipe as negative.
Determine the individual rates (tank per minute):
Pipe A fills the tank in 15 minutes, so its rate is 1/15 per minute.
Pipe B fills the tank in 30 minutes, so its rate is 1/30 per minute.
Pipe C empties the tank in 20 minutes, so its rate is -1/20 per minute.
Calculate the net rate:
When all three are opened together, the net rate is the sum of their individual rates: Net Rate = 1/15 + 1/30 - 1/20
Find the common denominator (LCM of 15, 30, and 20 is 60):
Net Rate = (4/60) + (2/60) - (3/60)
Net Rate = (4 + 2 - 3) / 60
Net Rate = 3/60 = 1/20 tank per minute.
Find the total time:
Time to fill = 1 / (Net Rate)
Time to fill = 1 / (1/20) = 20 minutes.