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Pipes A, B and C can fill a tank in 30 hours, 36 hours and 28 hours, respectively. All the three pipes were opened
simultaneously. If A and C were closed 5 hours and 8 hours, respectively, before the tank was filled completely, then in how
many hours was the tank filled?
12
14
16
15
- Pipe A fills the tank in 30 hours, which means it fills 1/30 of the tank in an hour.
- Pipe B fills the tank in 36 hours, filling 1/36 of the tank in an hour.
- Pipe C fills the tank in 28 hours, filling 1/28 of the tank in an hour.
- All three pipes work together initially.
- A is closed 5 hours before the tank is full.
- C is closed 8 hours before the tank is full.
- Let's assume the tank is filled in "t" hours.
Working period:
- Pipe A works for (t - 5) hours.
- Pipe C works for (t - 8) hours.
- Pipe B works for the entire "t" hours.
Equation:
$$
(t - 5) \left(\frac{1}{30}\right) + t \left(\frac{1}{36}\right) + (t - 8) \left(\frac{1}{28}\right) = 1
Solving the equation gives t = 15 hours.
Option 4 (15) is correct.
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