A cistern that would normally be filled in 6 hours is now taking 4 hours more because of a leak. In how much time, will the leak empty the cistern?
A cistern that would normally be filled in 6 hours is now taking 4 hours more because of a leak. In how much time, will the leak empty the cistern?
1). 12 hours
2). 8 hours
3). 15 hours
4). 9 hours
1 answers
Time taken by the inlet pipe to fill the cistern = 6 hours
So, part of cistern filled by inlet pipe in 1 hour = 1/6
Time taken to fill the cistern with leak = 6 hours + 4 hours = 10 hours
part of cistern filled by inlet pipe with leak in 1 hour = 1/10
Let the leak take x hours to empty the filled tank.
If an inlet pipe can fill the tank in x hours, then the portion filled in 1 hour = 1/x
$(\begin{array}{l} \frac{1}{6}\; - \;\frac{1}{x}\; = \frac{1}{{10}}\\ \Rightarrow \;\frac{1}{6}\; - \frac{1}{{10}}\; = \frac{1}{x}\\ \Rightarrow \;\frac{{10\; - \;6}}{{60}}\; = \;\;\frac{1}{x}\\ \Rightarrow \;\frac{4}{{60}}\; = \;\frac{1}{x} \end{array})$
⇒ 4x = 60
⇒ x = 15 hours
∴Time taken by leak to empty the cistern = x = 15 hours