The amount of antifreeze in the radiator at the start is 10% of 5 litres, that is
0.1*5 = 0.5 litres.
If we remove x litres of liquid, then assuming the antifreeze is uniformly mixed in, 10% of the liquid we remove will be antifreeze, so we will also be removing 0.1x litres of antifreeze. Then we will add in x litres of antifreeze. Thus, after the removal and addition of antifreeze, the total amount of antifreeze will be
0.5 - 0.1x + x = 0.5 + 0.9x litres.
Our final goal is to have the antifreeze constitute 30% of the 5 litres of liquid, that is
0.3*5 = 1.5 litres.
Thus, we need to drain off and replace x such that the total is 1.5 litres, i.e.,
0.5 + 0.9x = 1.5
=> 0.9x = 1.5 - 0.5 = 1
=> x = 1/0.9 = 1/(9/10) = 10/9 = 1.111...
So 10/9=1.111... litres should be drained off.
