The average weight of some students in a group is 58 kg. If 8 students of average weight 54 kg leave the group, and 3 students weighing 53.6 kg, 54 kg and 57.4 kg join the group, then the average weight of the remaining students in the group will increase by 575 g. The number of students, initially, in the group is

Let n be initial number of students. Total weight = 58n. After 8 leave and 3 join, new total = 58n - 8×54 + 53.6 + 54 + 57.4 = 58n - 432 + 165 = 58n - 267. New average: (58n - 267) ÷ (n - 5) = 58.575. Solving: 58n - 267 = 58.575(n - 5) = 58.575n - 292.875, which gives 0.575n = 25.875, so n = 45. Options A (35), C (50), and D (40) are incorrect.