One Tap Fills a Bath in 12 Minutes and Another in 15 Minutes with a Waste Pipe Problem
Learn how to solve this Pipe and Cistern (Time and Work) problem using a simple step-by-step method. This question is important for CBSE, SSC, Banking, Railway and other competitive examinations.
Key Takeaways
- Learn how inlet and outlet pipes work together.
- Calculate work done in one minute.
- Solve pipe and cistern problems using the LCM method.
- Useful for school and competitive examinations.
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Question
One tap fills a bath in 12 minutes and another tap fills it in 15 minutes. The wastepipe can empty the bath in 10 minutes. If both taps are turned on while the wastepipe is accidentally left open, in how much time will the bath be completely filled?
Step-by-Step Solution
Let the two taps be A and B, and the wastepipe be C.
Time taken by Tap A = 12 minutes
Time taken by Tap B = 15 minutes
Time taken by Wastepipe C = 10 minutes
Work Done in One Minute
Tap A = 1 12
Tap B = 1 15
Wastepipe C = 1 10
Net Work Done in One Minute
1 12 + 1 15 − 1 10
= 5 + 4 − 6 60
= 3 60 = 1 20
Therefore, the bath is filled at the rate of 1/20 of the bath per minute.
Final Answer
The net work done by both taps and the wastepipe together is
1 20 bath per minute.
Hence, the time required to fill the bath is
20 Minutes
Shortcut Method
You can solve this question quickly by taking the LCM of 12, 15, and 10, which is 60.
Assume the capacity of the bath is 60 units.
- Tap A fills 5 units per minute.
- Tap B fills 4 units per minute.
- Wastepipe empties 6 units per minute.
Net work per minute = 5 + 4 − 6 = 3 units
Time required
60 3 = 20 minutes
Exam Tips
- ✔ Inlet pipes are considered positive work.
- ✔ Outlet pipes are considered negative work.
- ✔ Find the LCM of all given times for quicker calculations.
- ✔ Add the filling rates and subtract the emptying rate.
- ✔ Finally, take the reciprocal of the net work to obtain the required time.
Practice Question
One pipe fills a tank in 8 hours, another fills it in 12 hours, and a wastepipe empties it in 24 hours. If all three are opened together, how long will it take to fill the tank?
Key Formula
Net Work = Sum of Filling Rates − Sum of Emptying Rates
Frequently Asked Questions (FAQs)
1. What is the formula used to solve pipe and cistern problems?
The net work done in one minute is calculated by adding the filling rates of all inlet pipes and subtracting the emptying rates of outlet pipes.
Net Work = Filling Rate − Emptying Rate
2. Why is the wastepipe subtracted?
The wastepipe removes water from the bath. Therefore, its work is considered negative and is subtracted from the total filling rate.
3. What is the final answer to this question?
The bath will be completely filled in 20 minutes.
4. Which examinations include this type of question?
Pipe and Cistern questions are frequently asked in SSC, Banking, Railway, NDA, CDS, State PSC, UPSC, and other competitive examinations.
Quick Revision
- ✔ Tap A fills the bath in 12 minutes.
- ✔ Tap B fills the bath in 15 minutes.
- ✔ Wastepipe empties the bath in 10 minutes.
- ✔ Net work done in one minute = 1/20 of the bath.
- ✔ Total time required = 20 minutes.
Summary
| Particular | Value |
|---|---|
| Tap A | 12 Minutes |
| Tap B | 15 Minutes |
| Wastepipe | 10 Minutes |
| Net Work | 1/20 Bath per Minute |
| Answer | 20 Minutes |
Conclusion
Pipe and Cistern questions become easy once you calculate the work done in one minute by each pipe. Add the filling rates, subtract the emptying rate, and take the reciprocal of the net work to find the required time. In this problem, the bath is filled completely in 20 minutes.