A bucket contains a mixture of two liquids P and Q in the ratio 5 : 2. If 14 liters of the mixture is taken out and 7 liters of liquid Q is added to the bucket, the ratio of P to Q becomes 2 : 1. Find the initial quantity of liquid P in the bucket.

Solution

Solution: Let the initial amounts be P = 5x and Q = 2x. Removing 14 litres in the ratio 5:2 removes 10 litres of P and 4 litres of Q. After removal, P = \(5x-10\) and Q = \(2x-4\). Adding 7 litres of Q gives Q = \(2x+3\). Using the new ratio, \(\frac{5x-10}{2x+3}=2\Rightarrow5x-10=4x+6\Rightarrow x=16\). Initial quantity of P \(=5x=80\) litres. Trick: Remove each component according to the original ratio before adding the extra liquid.