A leak empties a full tank in $20$ hr. An inlet admitting $3$ L/min is opened with the leak; the tank now…
A leak empties a full tank in $20$ hr. An inlet admitting $3$ L/min is opened with the leak; the tank now empties in $30$ hr. The capacity of the tank (in litres) is:
$10\,800$
$12\,000$
$14\,400$
$18\,000$
Solution
Leak rate $= \dfrac{1}{20}$ tank/hr. With inlet, net empty rate $= \dfrac{1}{30}$ tank/hr. So inlet rate $= \dfrac{1}{20} - \dfrac{1}{30} = \dfrac{3 - 2}{60} = \dfrac{1}{60}$ tank/hr. Inlet flow $= 3$ L/min $= 180$ L/hr. So $\dfrac{1}{60}$ tank $= 180$ L $\Rightarrow$ capacity $= 60 \times 180 = 10\,800$ L.