The weight of two persons N and A are in the ratio of 4 : 5. A's weight increased by 20% and the total weight of N and A together became 135 kg with an increase of 25%. By what percent did the weight of N increase?

Let initial weights be 4x and 5x (total 9x). After 25% increase, new total is 135 kg, so original total = 135/1.25 = 108 kg. Therefore 9x = 108, x = 12. Initial: N = 48 kg, A = 60 kg. A's new weight = 60 × 1.2 = 72 kg. New total = 135 kg, so N's new weight = 135 - 72 = 63 kg. N's increase = 63 - 48 = 15 kg. Percentage increase = (15/48) × 100 = 31.25%.