In a class of 35 students, the average marks is 72. The average marks of the boys is 75 and that of the girls is 68. Later, 5 new boys join the class. As a result, the average marks of all boys becomes 76 and the overall class average increases by 1 mark. Find the average marks of the 5 new boys.

ATQ, Let original number of boys = b, girls = g. We are given: b + g = 35. Total marks of all students initially = 35 × 72 = 2,520. Total marks of boys = 75b. Total marks of girls = 68g. So: 75b + 68g = 2,520. But g = 35 − b. ⇒ 75b + 68(35 − b) = 2,520 ⇒ 75b + 2,380 − 68b = 2,520 ⇒ 7b + 2,380 = 2,520 ⇒ 7b = 140 ⇒ b = 20. Therefore g = 35 − 20 = 15. So originally: Boys = 20, Girls = 15. Now 5 new boys join: New number of boys = 25. Let total marks of the 5 new boys = S. Original total marks of boys = 75 × 20 = 1,500. Given new average of boys = 76: (1,500 + S)/25 = 76 ⇒ 1,500 + S = 25 × 76 = 1,900 ⇒ S = 400. Average marks of the 5 new boys = 400/5 = 80. Check overall average: New total students = 40. Initial total marks = 2,520. New total = 2,520 + 400 = 2,920. New average = 2,920/40 = 73, which is 1 more than 72 (as given). Hence, Average marks of new 5 boys = 80.