A jar contains a mixture of two liquids A and B in the ratio 3: 1. When 16 liters of the mixture is taken out and 9 liters of liquid B is poured into the jar, the ratio becomes 3: 4. How many liters of liquid A was contained in the jar initially?

Solution

Solution: Let the initial mixture be V liters. Initially, A \(=\frac{3V}{4}\) and B \(=\frac V4\). Removing 16 liters removes 12 liters of A and 4 liters of B. After adding 9 liters of B, the amounts are A \(=\frac{3V}{4}-12\) and B \(=\frac V4+5\). Using the new ratio, \(\frac{\frac{3V}{4}-12}{\frac V4+5}=\frac34\), which gives \(V=28\). Initial A \(=\frac34\times28=21\) liters. Trick: Removing a mixture in the ratio 3:1 removes A and B in that same ratio.