SSC CGL Exam > SSC CGL Questions > When pipes A and C were open, the tank was fi...
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When pipes A and C were open, the tank was filled in 50 minutes. If Pipe A can fill the tank in 30 minutes, in how many minutes can Pipe C empty the filled tank?
- a)60
- b)75
- c)90
- d)120
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
When pipes A and C were open, the tank was filled in 50 minutes. If Pi...
Understanding the Problem
To solve the problem, we need to analyze the rates at which pipes A and C fill and empty the tank.
Filling Rate of Pipe A
- Pipe A can fill the tank in 30 minutes.
- Therefore, the rate of Pipe A is 1 tank/30 minutes or 1/30 tank per minute.
Combined Rate of Pipes A and C
- When both pipes A and C are open, they fill the tank in 50 minutes.
- Thus, their combined rate is 1 tank/50 minutes or 1/50 tank per minute.
Calculating the Rate of Pipe C
- Let the rate of Pipe C be x tanks per minute.
- The equation for their combined rates can be set up as follows:
(Rate of A) + (Rate of C) = (Combined Rate)
1/30 + x = 1/50
- To find x, we first convert the fractions to a common denominator, which is 150:
5/150 + x = 3/150
- Solving for x gives us:
x = 3/150 - 5/150 = -2/150
- This means Pipe C has a rate of -2/150 tanks per minute, indicating it empties the tank at this rate.
Time Taken by Pipe C to Empty the Tank
- To find out how long it takes for Pipe C to empty the full tank, we can calculate:
Time = 1 tank / (2/150 tanks per minute) = 150/2 = 75 minutes.
Conclusion
Thus, Pipe C can empty the filled tank in 75 minutes, making option 'B' the correct answer.
To solve the problem, we need to analyze the rates at which pipes A and C fill and empty the tank.
Filling Rate of Pipe A
- Pipe A can fill the tank in 30 minutes.
- Therefore, the rate of Pipe A is 1 tank/30 minutes or 1/30 tank per minute.
Combined Rate of Pipes A and C
- When both pipes A and C are open, they fill the tank in 50 minutes.
- Thus, their combined rate is 1 tank/50 minutes or 1/50 tank per minute.
Calculating the Rate of Pipe C
- Let the rate of Pipe C be x tanks per minute.
- The equation for their combined rates can be set up as follows:
(Rate of A) + (Rate of C) = (Combined Rate)
1/30 + x = 1/50
- To find x, we first convert the fractions to a common denominator, which is 150:
5/150 + x = 3/150
- Solving for x gives us:
x = 3/150 - 5/150 = -2/150
- This means Pipe C has a rate of -2/150 tanks per minute, indicating it empties the tank at this rate.
Time Taken by Pipe C to Empty the Tank
- To find out how long it takes for Pipe C to empty the full tank, we can calculate:
Time = 1 tank / (2/150 tanks per minute) = 150/2 = 75 minutes.
Conclusion
Thus, Pipe C can empty the filled tank in 75 minutes, making option 'B' the correct answer.
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Community Answer
When pipes A and C were open, the tank was filled in 50 minutes. If Pi...
Therefore, Pipe C can empty the filled tank in 75 minutes.
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When pipes A and C were open, the tank was filled in 50 minutes. If Pipe A can fill the tank in 30 minutes, in how many minutes can Pipe C empty the filled tank?a)60b)75c)90d)120Correct answer is option 'B'. Can you explain this answer?
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