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Pipes P and Q together can fill a tank in 80 minutes. If Pipe P alone can fill the tank in 120 minutes, in how many minutes can Pipe Q alone fill 75% of the tank?
- a)100
- b)120
- c)140
- d)180
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Pipes P and Q together can fill a tank in 80 minutes. If Pipe P alone ...
Pipe Q alone can fill the tank in
Hence, Option D is correct.
Hence, Option D is correct.
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Pipes P and Q together can fill a tank in 80 minutes. If Pipe P alone ...
Understanding the Problem
To solve the problem, we need to find out how long Pipe Q takes to fill 75% of the tank, given the rates at which Pipes P and Q can fill the tank.
Filling Rates of Pipes
- Pipe P can fill the tank in 120 minutes.
- Therefore, the rate of Pipe P = 1 tank / 120 minutes = 1/120 tank per minute.
- Pipes P and Q together can fill the tank in 80 minutes.
- Therefore, their combined rate = 1 tank / 80 minutes = 1/80 tank per minute.
Calculating the Rate of Pipe Q
- Let the rate of Pipe Q be denoted as R_Q.
- The equation for the combined rates of Pipes P and Q is:
1/120 + R_Q = 1/80
- To find R_Q, we need to solve this equation:
R_Q = 1/80 - 1/120
- Finding a common denominator (240):
R_Q = (3/240) - (2/240) = 1/240
- Thus, Pipe Q can fill the tank at a rate of 1/240 tank per minute.
Time Taken by Pipe Q to Fill 75% of the Tank
- To fill 75% of the tank, we calculate the time required:
Time = Volume / Rate
Time = 0.75 tank / (1/240 tank per minute) = 0.75 * 240 = 180 minutes
Conclusion
Therefore, Pipe Q alone can fill 75% of the tank in 180 minutes, which corresponds to option 'D'.
To solve the problem, we need to find out how long Pipe Q takes to fill 75% of the tank, given the rates at which Pipes P and Q can fill the tank.
Filling Rates of Pipes
- Pipe P can fill the tank in 120 minutes.
- Therefore, the rate of Pipe P = 1 tank / 120 minutes = 1/120 tank per minute.
- Pipes P and Q together can fill the tank in 80 minutes.
- Therefore, their combined rate = 1 tank / 80 minutes = 1/80 tank per minute.
Calculating the Rate of Pipe Q
- Let the rate of Pipe Q be denoted as R_Q.
- The equation for the combined rates of Pipes P and Q is:
1/120 + R_Q = 1/80
- To find R_Q, we need to solve this equation:
R_Q = 1/80 - 1/120
- Finding a common denominator (240):
R_Q = (3/240) - (2/240) = 1/240
- Thus, Pipe Q can fill the tank at a rate of 1/240 tank per minute.
Time Taken by Pipe Q to Fill 75% of the Tank
- To fill 75% of the tank, we calculate the time required:
Time = Volume / Rate
Time = 0.75 tank / (1/240 tank per minute) = 0.75 * 240 = 180 minutes
Conclusion
Therefore, Pipe Q alone can fill 75% of the tank in 180 minutes, which corresponds to option 'D'.
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Pipes P and Q together can fill a tank in 80 minutes. If Pipe P alone can fill the tank in 120 minutes, in how many minutes can Pipe Q alone fill 75% of the tank?a)100b)120c)140d)180Correct answer is option 'D'. Can you explain this answer?
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