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Two inlet pipes can separately fill a cistern completely in 8 hours and 10 hours respectively. They are operated for 2 hours, after
which the second pipe is closed, and an outlet pipe which can drain out water from the full cistern in 20 hours is opened. How
much time will it take to fill the cistern completely from the instant of opening the outlet pipe?
7 hours
8 hours
7 hours 20 minutes
8 hours 40 minutes
- Pipe A fills the cistern in 8 hours, so in one hour, it fills 1/8 of the cistern.
- Pipe B fills the cistern in 10 hours, so in one hour, it fills 1/10 of the cistern.
- Both pipes run for 2 hours:
- In 2 hours, both pipes together fill: 2×(18+110)=2×940=920 of the cistern.
- The remaining cistern (1−920) is 1120.
- Pipe A continues with an outlet pipe that drains in 20 hours:
- Pipe A fills 18 per hour. Outlet drains 120 per hour.
- The net fill rate is: 18−120=540−240=340 per hour.
- Time to fill the remaining 1120 at 340 per hour:
- Time = 1120340 = 1120×403=223 hours = 7 hours 20 minutes.
- Option 3: 7 hours 20 minutes is correct.
-
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