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Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank?
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Pipes A and B together can fill a tank in 6 hours and pipe C alone fil...
Understanding the Problem
To solve this, we first need to determine the rates at which the pipes A, B, and C fill the tank.
Filling Rates
- **Pipes A and B together**: They can fill the tank in 6 hours, so their combined rate is:
- Rate of A + B = 1 tank / 6 hours = 1/6 tanks per hour.
- **Pipe C alone**: Fills the tank in 15 hours, hence:
- Rate of C = 1 tank / 15 hours = 1/15 tanks per hour.
Combined Rate of A, B, and C
- To find the combined rate of A, B, and C, we add their rates:
- Rate of A + B + C = (1/6 + 1/15) tanks per hour.
To find a common denominator (30):
- 1/6 = 5/30
- 1/15 = 2/30
Thus,
Rate of A + B + C = (5/30 + 2/30) = 7/30 tanks per hour.
Work Done in 3 Hours
- In 3 hours, the amount of the tank filled by A, B, and C is:
- Work done = Rate × Time = (7/30) × 3 = 7/10 tanks.
Remaining Work
- After 3 hours, the remaining work to fill the tank is:
- Remaining = 1 - 7/10 = 3/10 tanks.
Rate of A and B Together
- The rate of A and B together is already calculated as 1/6 tanks per hour.
Time Required to Fill Remaining Tank
- To find the time required for A and B to fill the remaining 3/10 tanks:
- Time = Remaining work / Rate = (3/10) / (1/6) = 3/10 × 6/1 = 18/10 = 1.8 hours.
Conclusion
Thus, pipes A and B together can fill the remaining tank in **1.8 hours**.
To solve this, we first need to determine the rates at which the pipes A, B, and C fill the tank.
Filling Rates
- **Pipes A and B together**: They can fill the tank in 6 hours, so their combined rate is:
- Rate of A + B = 1 tank / 6 hours = 1/6 tanks per hour.
- **Pipe C alone**: Fills the tank in 15 hours, hence:
- Rate of C = 1 tank / 15 hours = 1/15 tanks per hour.
Combined Rate of A, B, and C
- To find the combined rate of A, B, and C, we add their rates:
- Rate of A + B + C = (1/6 + 1/15) tanks per hour.
To find a common denominator (30):
- 1/6 = 5/30
- 1/15 = 2/30
Thus,
Rate of A + B + C = (5/30 + 2/30) = 7/30 tanks per hour.
Work Done in 3 Hours
- In 3 hours, the amount of the tank filled by A, B, and C is:
- Work done = Rate × Time = (7/30) × 3 = 7/10 tanks.
Remaining Work
- After 3 hours, the remaining work to fill the tank is:
- Remaining = 1 - 7/10 = 3/10 tanks.
Rate of A and B Together
- The rate of A and B together is already calculated as 1/6 tanks per hour.
Time Required to Fill Remaining Tank
- To find the time required for A and B to fill the remaining 3/10 tanks:
- Time = Remaining work / Rate = (3/10) / (1/6) = 3/10 × 6/1 = 18/10 = 1.8 hours.
Conclusion
Thus, pipes A and B together can fill the remaining tank in **1.8 hours**.
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Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank?
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Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank? 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 Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank?.
Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank? 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 Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pipes A and B together can fill a tank in 6 hours and pipe C alone fills the tank in 15 hours. If pipe A, B and C together can open simultaneously and after 3 hours pipe C is closed, in how many hours A and B together can fill the remaining tank?.
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