The original amount of water is w and the original amount of alcohol is a. It should be clear that a = 2w.

You need to add a certain amount of water (k) to make the ratio 1:2, in other words, so that w + k = 2a.

From here, we can see that w + k = 2(2w), so k = 3w.

Since we know there were originally 60L in the mixture, in the ratio of 2:1, that means there was originally (1/3)60 = 20 L of water. So you have to add three times that to get the ratio you want. Therefore, add 60L of water.