In two vessels ratio of milk and water is (5:3) and (2:3) respectively. In what ratio they should mix so that in resultant mixture quantity of milk and water becomes equal?

Vessel 1 has milk:water = 5:3, so milk fraction = 5/8. Vessel 2 has milk:water = 2:3, so milk fraction = 2/5. Let x and y be parts taken from vessels 1 and 2 respectively. For equal milk and water in final mixture: (5/8)x + (2/5)y = (3/8)x + (3/5)y. Simplifying: (5/8 - 3/8)x = (3/5 - 2/5)y, so (2/8)x = (1/5)y, giving x/y = (1/5)×(8/2) = 4/5. The vessels should be mixed in ratio 4:5.