Three containers have their volumes in the ratio 3 : 4 : 5. They are full of milk and water. The mixture contains milk and water in the ratio of (4 : 1), (3 : 1) and (5 : 2) respectively. The ratio of milk and water in the fourth container contains all the above three mixtures is:

Solution: The volumes of the milk and the water in the three containers are in the ratio 3:4:5. The milk and the water in the three containers are in the ratio 4:1, 3:1, and 5:2 respectively.
Step 1 – calculate the milk fraction in the containers: Container 1: milk fraction is 4/5, milk in the container = 3 × 4/5 = 12/5. Container 2: milk fraction is 3/4, milk in the container = 4 × 3/4 = 3. Container 3: milk fraction is 5/7, milk in the container = 5 × 5/7 = 25/7.
Step 2 – calculate the fraction of the water in the containers: Container 1: fraction of the water = 1 - 4/5 = 1/5, water in the container = 3 × 1/5 = 3/5. Container 2: fraction of the water = 1 - 3/4 = 1/4, water in the container = 4 × 1/4 = 1. Container 3: fraction of the water = 1 - 5/7 = 2/7, water in the container = 5 × 2/7 = 10/7.
Step 3 – calculate the total milk and the total water in the containers: Total milk = 12/5 + 3 + 25/7 = 314/35. Total water = 3/5 + 1 + 10/7 = 106/35.
Step 4 – calculate the final ratio: Milk : Water = 314 : 106 = 157 : 53.Answer: (C) 157 : 53