Let x be the mass of sugar needed to make a 20% solution.

We know that the total mass of the solution is 270 g.

Since the solution is 20% sugar, the mass of sugar in the solution is 0.20 * 270 = 54 g.

Now, let's say y is the mass of the 10% solution needed to make a solution with a total mass of 270 g.

Since the 10% solution is 10% sugar, the mass of sugar in the 10% solution is 0.10 * y.

To achieve a total of 54 g of sugar in the final solution, we need to add x grams of sugar from the pure sugar and (54 - x) grams of sugar from the 10% solution.

To achieve a total mass of 270 g in the final solution, we must have:

x + y = 270 g (equation 1)
0.10y + x = 54 g (equation 2)

Solving equations 1 and 2 simultaneously, we get:
y = 216g
x = 54g

Therefore, the mass of sugar needed to make a 20% solution is 54g.