Question : Tap A can fill an empty tank in 8 hours if no other tap is open, and tap B can empty the same tank, when filled, in 12 hours, when no other tap is open. Find the time taken to fill the same tank, when empty, if both the taps are opened together.
Option 1: 12 hours
Option 2: 16 hours
Option 3: 24 hours
Option 4: 36 hours
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Correct Answer: 24 hours
Solution : Let the rate at which tap A fills the tank as A and the rate at which tap B empties the tank as B. Given that tap A can fill the tank in 8 hours, A = $\frac{1}{8}$ tanks per hour. Similarly, tap B can empty the tank in 12 hours, B = $\frac{1}{12}$ tanks per hour. When both taps are opened together, the net rate of filling the tank = $\frac{1}{8} - \frac{1}{12}=\frac{1}{24}$ tanks per hour. The time is taken to fill the tank when both taps are opened together = $\frac{1}{\frac{1}{24}}$ = 24 hours Hence, the correct answer is 24 hours.
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