A vessel is full of mixture of spirit and water in which there is 20% of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12%, find the total quantity in the vessel (in ltrs).

Question: A vessel is full of mixture of spirit and water in which there is 20% of spirit. 5 litres are drawn off and the vessel is filled up with water. If the spirit is now 12%, find the total quantity in the vessel (in ltrs).

Solution:
Let the total mixture be x liters.
It contains 20% spirit i.e. 0.2 of the total mixture.
When 5 liters are drawn off, quantity of spirit removed = 0.2(5) = 1 liters.
Remaining spirit = 0.2x - 1.
Also remaining spirit = 0.12x.

∴ 0.2x - 1 = 0.12x
⇒ 0.08x = 1
⇒ x = 1/0.08
⇒ x = 12.5