Question : An inlet pipe can fill an empty tank in 3.6 hours, while an outlet pipe can drain a completely filled tank in 6.3 hours. If both the pipes are opened simultaneously when the tank is empty, in how many hours will the tank get completely filled?
Option 1: 9
Option 2: 8.4
Option 3: 8.1
Option 4: 8.7
Correct Answer: 8.4
Solution :
The rate at which the inlet pipe can fill the tank is 1 tank per 3.6 hours, or $\frac{1}{3.6}$ tanks per hour.
The rate at which the outlet pipe can drain the tank is 1 tank per 6.3 hours, or $\frac{1}{6.3}$ tanks per hour.
When both pipes are opened simultaneously, the net rate of filling the tank is the rate of the inlet pipe minus the rate of the outlet pipe.
$\text{Net rate} = \frac{1}{3.6} - \frac{1}{6.3}$
⇒ $\text{Time} = \frac{1}{\text{Net rate}}$
⇒ $\text{Time} = \frac{1}{\frac{1}{3.6} - \frac{1}{6.3}}$
⇒ $\text{Time} = \frac{1}{\frac{5}{18} - \frac{10}{63}}= \frac{1}{\frac{5}{42} }= \frac{42}{5}$
⇒ $\text{Time} =8.4$ hours
Hence, the correct answer is 8.4.
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