Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second. In what ratio should the contents of these two vessels be mixed such that the resultant mixture has milk and water in the ratio of 2:5?

Vessel 1 has milk:water = 4:9, so milk fraction = 4/13. Vessel 2 has milk:water = 2:7, so milk fraction = 2/9. Target mixture needs milk:water = 2:5, so milk fraction = 2/7. Using allegation: (2/7 - 2/9) : (4/13 - 2/7) = (4/63) : (2/91) = (4/63) × (91/2) = 182/126 = 26:9. Mix in ratio 26:9 (Vessel 1 : Vessel 2). Option A is correct. Other ratios don't satisfy the allegation calculation.