A vessel contains a mixture of milk and water in the ratio 5 : 3. 32 litres of this mixture is drawn off and replaced with water, after which the…

Let the total volume be T. Milk fraction = 5/8, so milk = (5/8)T. Since only water is added back, the total volume stays T, and after removal+replacement the milk left is (5/8)(T−32). The new ratio milk:total = 5:(5+7) = 5:12, so (5/8)(T−32)/T = 5/12 → (T−32)/T = 2/3 → T = 96. Initial milk = (5/8)×96 = 60 litres. Check: removing 32 L takes out 20 L milk, 12 L water, leaving 40 milk : 24 water; adding 32 L water gives 40:56 = 5:7. ✓