Two containers with equal capacity have milk and water in the ratio of 3 : 4 and 3 : 1 respectively. If both the containers are emptied into a bigger container having the capacity to contain the whole mixture, then what is the ratio of milk to water in the bigger container?

Let the capacity of each container be the same. Container 1 has milk:water = 3:4, so milk = 3x, water = 4x, total = 7x. Container 2 has milk:water = 3:1, so milk = 3y, water = 1y, total = 4y. Since capacities are equal: 7x = 4y, giving y = 7x/4. Total milk = 3x + 3y = 3x + 3(7x/4) = 3x + 21x/4 = 33x/4. Total water = 4x + 1y = 4x + 7x/4 = 23x/4. Ratio of milk:water = (33x/4) : (23x/4) = 33:23.