The volume of the 25% sugar solution needed is 200 liters.
Let the volume of the 25% solution that should be added = x
set up the equation as follows;
x(0.25) + 0.5(500 - x) = 500(0.4)
solve for x as shown below;
0.25x + 250 - 0.5x = 200
-0.25x = 200 - 250
-0.25x = -50
x = 50/0.25
x = 200 Liters
Thus, the volume of the 25% sugar solution needed is 200 liters.
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