I have 30 cubic meter solution of caustic with concentration of 77g/L.
I want to maintain its concentration up to 90g/L by adding 50% caustic solution.
How much 50% caustic required?

1. Find the equivalent of 50% caustic solution in terms of g/L.
2. Use the equation for the number of moles.

n_1 + n_2 = n_t

n1 is the number of moles in the 3m^3 solution that you have;
n2 is the number of moles that you are adding; and
nt is the total number of moles after adding the two moles and will be in the 90g/L solution.

Then substitute those by using the equation:

Moles\ =\ Concentration\ \times\ Volume