A bucket contains a mixture of two liquids P and Q are in the ratio 4 : 1. When 10 liters of the mixture is taken out and 10 liters of liquid Q is poured into the bucket, the ratio becomes 2 : 3. How many liters of liquid P was contained in the bucket?

Solution

Solution: Let the initial quantities be P = 4x and Q = x. The total mixture is 5x liters. Removing 10 liters in the ratio 4:1 removes 8 liters of P and 2 liters of Q. After adding 10 liters of Q, the quantities are P = \(4x-8\) and Q = \(x-2+10=x+8\). Using the new ratio, \(\frac{4x-8}{x+8}=\frac23\). Thus, \(12x-24=2x+16\Rightarrow10x=40\Rightarrow x=4\). Initial P \(=4x=16\) liters. Trick: Remove each component in its original ratio before adding the new liquid.