Two equal vessels A and B contain 60% of sugar and 40% of sugar respectively and the remaining Water. In which 40 kg of mixture is taken out from vessel A and replaced into vessel B. Find the initial quantity of vessel if the final ratio of sugar and Water in vessel B is 16: 19?

Let x be initial quantity of each vessel. Vessel A: 60% sugar, 40% water. Vessel B: 40% sugar, 60% water. After removing 40 kg from A (containing 24 kg sugar, 16 kg water) and adding to B: Vessel B has (0.4x + 24) kg sugar and (0.6x + 16) kg water. The ratio 16:19 means (0.4x + 24)/(0.6x + 16) = 16/19. Cross-multiplying: 7.6x + 456 = 9.6x + 256, giving 2x = 200, so x = 100. Option C is correct.