A vessel contains a mixture of milk and water in the ratio 5 : 3. When 16 litres of this mixture are taken out and replaced with pure water, the ratio of milk to water becomes 5 : 7. What was the initial quantity of the mixture in the vessel?

Let initial quantity of mixture = Q litres. Milk = (5/8)Q, Water = (3/8)Q. When 16 L mixture is removed, milk and water removed are in same ratio 5 : 3: Milk removed = (5/8)*16 = 10 L Water removed = (3/8)*16 = 6 L Remaining after removal: Milk = (5/8)Q − 10 Water = (3/8)Q − 6 Then 16 L of pure water is added: New amount of water = (3/8)Q − 6 + 16 = (3/8)Q + 10 New ratio milk : water = 5 : 7: [(5/8)Q − 10] / [(3/8)Q + 10] = 5 / 7 Cross-multiply: 7[(5/8)Q − 10] = 5[(3/8)Q + 10] (35/8)Q − 70 = (15/8)Q + 50 Bring like terms together: (35/8Q − 15/8Q) = 50 + 70 (20/8)Q = 120 (5/2)Q = 120 Q = 120 * 2 / 5 = 48 Initial quantity of mixture = 48 litres.