Question

A cistern has a leak which would empty it in 10h.A tap is turned on which admits 4 lit/min into the cistern and it is now emptied in 15h.How much litres does the cistern hold?

Answer 1

Let us assume that the cistern can hold $x$ liters of water. Since the cistern empties in 10 hours, therefore, empty rate $=\frac{x}{10}$ lit/hr.

Given, fill rate $=4$ lit/min $=4\times60=240$ lit/hr

Resultant rate = fill rate - empty rate = $240-\frac{x}{10}$ lit/hr

Time required to fill the cistern with the new rate $=\frac{x}{240-\frac{x}{10}}=15$ hr

$$\begin{aligned} \frac{x}{240-\frac{x}{10}} &= 15 \\ \frac{10x}{2400-x} &= 15 \\ 10x &= 15\cdot(2400-x) \\ 10x &= 36000-15x \\ 10x+15x &= 36000 \\ 25x &= 36000 \\ x &= \frac{36000}{25}=\boxed{1440} \\ \end{aligned}$$

Hence the cistern holds 1400 liters of water.