In two vessels ratio of milk and water is 5:3 and 5:7 respectively. They are mixed together in 5:4 . Find the ratio of milk and water in the final mixture.

First find the fraction of milk and water in each vessel. Vessel 1 (5:3) has milk = 5/8, water = 3/8. Vessel 2 (5:7) has milk = 5/12, water = 7/12. When mixed in ratio 5:4, multiply each fraction by the mixing ratio and sum. Total milk = 5*(5/8) + 4*(5/12) = 115/24. Total water = 5*(3/8) + 4*(7/12) = 101/24. The ratio milk:water = 115:101.