That's wrong, realize as you add water to the mixture, the volume of the mixture increases as well. Thus if you added 10 ltr of water to the 50 ltr mixture you would get a 60 ltr mixture. made of 45 ltr milk and 15 ltr water. That's 25% water in the mixture, not the 20% water being asked.

So, from the start:

m = Milk

w = Water

x = amount of water to add

For the mixture without any additional water:

w = 5 ltr

m = 45 ltr

Thus :

(45 + (5 + x)) - ((45 + (5 + x)) * 8/10) = (5 + x)

(50 + x) - ((50 + x) * 8/10) = (5 + x)

(50 + x) - (40 + (x * 8/10)) = (5 + x)

(50 + x) = (5 + x) + (40 + (x * 8/10))

50 + x = 45 + x + (x * 8/10)

50 = 45 + (x * 8/10)

5 = x * 8/10

5 * 10/8 = x

6.25 = x

The new mixture = 56.25 ltr

And 20% of 56.25 = 11.25 ltr = 5 (original amount) + 6.25 (amount of water added)

Thus, How much water must be added to make water 20% in the given mixture?

6.25 ltr water