SSC CGL Exam > SSC CGL Questions > Pipes M and N can fill a tank in 30 and 120 m...
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Pipes M and N can fill a tank in 30 and 120 minutes respectively. If both the pipes are opened together, in how many minutes will the tank be filled?
- a)20
- b)24
- c)30
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Pipes M and N can fill a tank in 30 and 120 minutes respectively. If b...
Hence, Option B is correct.
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Pipes M and N can fill a tank in 30 and 120 minutes respectively. If b...
Understanding the Problem
To solve the problem, we first need to determine how much of the tank each pipe can fill in a minute.
Filling Rates of Pipes
- Pipe M fills the tank in 30 minutes. Therefore, in one minute, it fills:
- 1/30 of the tank.
- Pipe N fills the tank in 120 minutes. Therefore, in one minute, it fills:
- 1/120 of the tank.
Combined Filling Rate
When both pipes are opened together, we can add their filling rates:
- Combined filling rate = (1/30) + (1/120)
To add these fractions, we need a common denominator, which is 120:
- (1/30) = 4/120
- (1/120) = 1/120
Now, we can add the two:
- Combined filling rate = (4/120) + (1/120) = 5/120
This simplifies to:
- Combined filling rate = 1/24 of the tank per minute.
Calculating Time to Fill the Tank
Now that we know the combined filling rate, we can determine how long it takes to fill the entire tank:
- If both pipes together fill 1/24 of the tank in one minute, then to fill 1 tank:
- Time = 1 / (1/24) = 24 minutes.
Conclusion
Thus, if both pipes M and N are opened together, the tank will be filled in 24 minutes. The correct answer is option B.
To solve the problem, we first need to determine how much of the tank each pipe can fill in a minute.
Filling Rates of Pipes
- Pipe M fills the tank in 30 minutes. Therefore, in one minute, it fills:
- 1/30 of the tank.
- Pipe N fills the tank in 120 minutes. Therefore, in one minute, it fills:
- 1/120 of the tank.
Combined Filling Rate
When both pipes are opened together, we can add their filling rates:
- Combined filling rate = (1/30) + (1/120)
To add these fractions, we need a common denominator, which is 120:
- (1/30) = 4/120
- (1/120) = 1/120
Now, we can add the two:
- Combined filling rate = (4/120) + (1/120) = 5/120
This simplifies to:
- Combined filling rate = 1/24 of the tank per minute.
Calculating Time to Fill the Tank
Now that we know the combined filling rate, we can determine how long it takes to fill the entire tank:
- If both pipes together fill 1/24 of the tank in one minute, then to fill 1 tank:
- Time = 1 / (1/24) = 24 minutes.
Conclusion
Thus, if both pipes M and N are opened together, the tank will be filled in 24 minutes. The correct answer is option B.
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Pipes M and N can fill a tank in 30 and 120 minutes respectively. If both the pipes are opened together, in how many minutes will the tank be filled?a)20b)24c)30d)40Correct answer is option 'B'. Can you explain this answer?
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