A water tank is (3/5)th full. Pipe A can fill the tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Solution
Correct Answer: Option C
∴ Part of the tank filled by Pipe A in 1 minute = 1/10
∴ Part of the tank emptied by Pipe B in 1 minute = 1/6
∵ The rate at which the tank is emptied is more than the rate at which it filled,
When the tank is full
∴ Part of the tank emptied by both pipes in 1 minute \(= {\rm{\;}}\frac{1}{6} - \frac{1}{{10}}{\rm{\;}} = {\rm{\;}}\frac{1}{{15}}\)
∴ Time required by both the pipes to empty the tank \(= {\rm{\;}}\frac{1}{{\frac{1}{{15}}}}{\rm{\;}} = {\rm{\;}}15{\rm{\;minutes}}\)
Since the tank is (3/5)th full
∴ Time required by both the pipes to empty the tank \(= {\rm{\;}}\frac{3}{5} \times 15{\rm{\;}} = {\rm{\;}}9{\rm{\;minutes}}\)
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