A cistern is filled by a tap in 15 hours. Due to a leak in the bottom of the cistern, it takes 5 hours longer to fill the cistern. If the cistern is full how long will it take the leak to empty it?(assume rate of leakage will be constant).
Solution
Correct Answer: Option B
Tap fills the cistern in 15 hours
∴ part of cistern filled by the tap in 1 hour = 1/15
With the leak tap fills the cistern in 5 hours more, i.e. in 20 hours
∴ part of cistern filled by the tap in 1 hour with the leak = 1/20
∴ in 1 hour liquid flowing out through the leak \(= \;\left( {\frac{1}{{15}} - \frac{1}{{20}}} \right)\; = \;\frac{1}{{60}}\)
The full liquid will flow out through the leak in 60 hours
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