A vessel has a milk solution in which ratio of milk and water is 4 : 1 by adding some water into it ,the ratio of milk and water become 4:3,on replacing 14 litre of this solution with pure milk the ratio of milk and water changed to 5:3.what is the volume of water added?

Let initial volume = x. Initial milk:water = 4:1, so milk = 4x/5, water = x/5. After adding water (32 liters), ratio becomes 4:3, so milk = 4(x+32)/7, water = 3(x+32)/7. Equating milk: 4x/5 = 4(x+32)/7 gives x = 80. Initial water = 16. Final: 80+32 = 112 liters with milk = 64, water = 48. After replacing 14 liters with pure milk: milk = 64 - 8 + 14 = 70, water = 48 - 6 = 42. Ratio 70:42 = 5:3. Correct.