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Pipe A alone fill the tank in 24 hours and the efficiency of pipe A and B in the ratio of 5:3. If pipes A and B are opened together and at the end of each hour one-fourth of water added by A and B together in a hour is leaked from the tank, in how many hours are required to fill the tank completely?
20 Hr.
10 Hr.
8 Hr.
14 Hr.
15 Hr.
- Pipe A can fill the tank in 24 hours. Therefore, Pipe A fills 1/24 of the tank per hour.
- The efficiency of pipes A and B is in the ratio of 5:3. Hence, Pipe B fills (3/5) of what Pipe A fills per hour.
- Pipe B fills (3/5) * (1/24) = 1/40 of the tank per hour.
- Together, A and B fill (1/24 + 1/40) = 1/15 of the tank per hour.
- Due to leakage, one-fourth of the water added each hour by both pipes is lost.
- Effective filling per hour = (1/15) - (1/4) * (1/15) = (3/60) = 1/20 of the tank.
- Thus, the time required to fill the tank completely is 20 hours.
So, the correct option is:
- Option 1: 20 Hr.
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