1.

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 hours2). 8 hours3). 15 hours4). 9 hours

Answer»

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


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