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One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened?
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One tap can fill a cistern in 30 min and another can empty the cistern...
Understanding the Problem
To solve the problem, we need to determine the rates at which the taps fill and empty the cistern and then combine these rates.
Rates of the Taps
- Filling Tap: It can fill the cistern in 30 minutes.
- Rate = 1 cistern / 30 minutes = 1/30 cisterns per minute.
- Emptying Tap: It can empty the cistern in 1.5 hours (90 minutes).
- Rate = 1 cistern / 90 minutes = 1/90 cisterns per minute.
Combining the Rates
When both taps are opened, the filling tap adds water while the emptying tap takes it away. We combine their rates as follows:
- Net Rate = Rate of Filling Tap - Rate of Emptying Tap
- Net Rate = (1/30) - (1/90)
To perform this subtraction, we need a common denominator, which is 90:
- (1/30) = 3/90
- (1/90) remains the same.
Thus,
- Net Rate = (3/90) - (1/90) = 2/90 = 1/45 cisterns per minute.
Calculating the Time to Fill the Cistern
Since the net rate of filling the cistern is 1/45 cisterns per minute, we can find the time taken to fill one full cistern:
- Time = 1 cistern / (1/45 cisterns per minute) = 45 minutes.
Conclusion
When both taps are opened, they will take 45 minutes to fill the cistern.
To solve the problem, we need to determine the rates at which the taps fill and empty the cistern and then combine these rates.
Rates of the Taps
- Filling Tap: It can fill the cistern in 30 minutes.
- Rate = 1 cistern / 30 minutes = 1/30 cisterns per minute.
- Emptying Tap: It can empty the cistern in 1.5 hours (90 minutes).
- Rate = 1 cistern / 90 minutes = 1/90 cisterns per minute.
Combining the Rates
When both taps are opened, the filling tap adds water while the emptying tap takes it away. We combine their rates as follows:
- Net Rate = Rate of Filling Tap - Rate of Emptying Tap
- Net Rate = (1/30) - (1/90)
To perform this subtraction, we need a common denominator, which is 90:
- (1/30) = 3/90
- (1/90) remains the same.
Thus,
- Net Rate = (3/90) - (1/90) = 2/90 = 1/45 cisterns per minute.
Calculating the Time to Fill the Cistern
Since the net rate of filling the cistern is 1/45 cisterns per minute, we can find the time taken to fill one full cistern:
- Time = 1 cistern / (1/45 cisterns per minute) = 45 minutes.
Conclusion
When both taps are opened, they will take 45 minutes to fill the cistern.
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One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened?
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One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened?.
One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for One tap can fill a cistern in 30 min and another can empty the cistern in 1 1/2 hours. How long will they take to fill the cistern if both the taps are opened?.
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