A mixture contains milk and water, where the difference between the quantities of milk and water is 20% of the total mixture, which is 180
ml. If adding 18 ml of water changes the ratio of water to milk to 5:6, what is the initial quantity of milk in the mixture?

Difference between initial quantities of milk and water = 0.2 X 180 = 36 ml Let the initial quantity of milk in the solution be 'a' ml. So, initial quantity of water in the solution = (a + 36) ml or, (a - 36) ml Case I: quantity of water = (a + 36) ml (a + 36 + 18) ÷ a = (5/6) Or, 6 X (a + 54) = 5a Or, 6a + 324 = 5a So, 'a' = - 324 which is not possible, since quantities can't be negative. Case II: quantity of water = (a - 36) ml (a - 36 + 18) ÷ a = (5/6) Or, 6 X (a - 18) = 5a Or, 6a - 108 = 5a So, 'a' = 108 Therefore, initial quantity of milk = 108 ml