Let a=amount in mL of the 90% alcohol mixture (10% water), w=amount of 100% pure water (0% alcohol).
a+w=270mL
Consider the amount of alcohol:
0.9a=0.05×270=13.5mL, a=13.5/0.9=15mL.
w=270-15=255mL.
So we need 255mL of pure water and 15mL of 90% alcohol mixture.
(Another way is to consider the amount of pure water:
0.1a+w=0.95×270=256.5,
0.1a+270-a=256.5mL,
13.5=0.9a, a=15mL, w=255mL.)