The total number of students in sections A and B of a class is 65. The ratio of the number of the students in A and B is 9 : 4. The average weight (in kg) of the students in section B is 25% more than that of the students in section A. If the average weight of all the students in the class is 98 kg, then what is the average weight (in kg) of the students in section A?

91

Ratio of number of students = 9 : 4   =   13R

ATQ, 13R = 65 ⇒ 1R = 5

Hence,

Number of students in A = 45

Number of students in B = 20

Now,

25% = \(\frac{1}{4}\)

Avg. weight of A and B = 4R, 5R

So

⇒ Total weight of all students in A = 45 × 4R

⇒ Total weight of all students in B = 20 × 5R and

⇒ Total weight of all students (A + B) = 65 × 98

Hence,

⇒ (45 × 4R) + (20 × 5R) = 65 × 98

⇒ 180 R + 100 R = 6370

⇒ 280 R = 6370

⇒ R = \(\frac{6370}{280}\) = \(\frac{637}{28}\)

Avg. of class of student A = \(\frac{637}{28}\) × 4 = 91