A vessel contains a mixture of milk and water in the ratio of 14 : 3.

\(\frac{milk}{water}\) = \(\frac{14}{3}\)

milk = \(\frac{14}{17}\)

water = \(\frac{3}{17}\)

25.5 litres of mixture is taken out = 25.5 = \(\frac{255}{10}\) = \(\frac{51}{2} \ litres\)

Remaining Milk = \(14x - \frac{14}{17}*\frac{51}{2}\) = \(14x-21 \ litres\)

Remaining Water = \(3x - \frac{3}{17}*\frac{51}{2}\) = \(3x-4.5 \ litres\)

Then, 2.5 litres of water and 5 litres of milk is added. Thus, final quantity of water and milk is:

Milk = \(14x-21+5\) = \(14x-16 \ litres\)

Water = \(3x-4.5+2.5\) = \(3x-2 \ litres\)

Resultant Mixture = \(14x-16+3x-2 \ litres\) = \(17x-18 \ litres\)

Given, resultant mixture contains 20% water:

\(0.2*(17x-18) = 3x-2\)
\(3.4x - 3.6 = 3x-2\)
\(0.4x = 1.6\)
\(x = 4\)

Thus, initial quantity of mixture was \(= 17x = 17*4 = 68 \ litres (C)\)