The average score in Mathematics of 90 students of section A and B of class IX was 63. The number of student in A were 10 more that those in B. The average score of student in A was 30% more than that of students in B. The average score of students in B is:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Students in }}A = 50 \cr & {\text{Students in }}B = 40 \cr & {\text{Total students}}:A:B = 9:5:4 \cr & \frac{{{\text{Average of }}A}}{{{\text{Average of }}B}} = \frac{{13x}}{{10x}} \cr & 9 \times 63 = 13x \times 5 + 10x \times 4 \cr & 567 = 65x + 40x \cr & 105x = 567 \cr & x = \frac{{567}}{{105}} \cr & x = \frac{{81}}{{15}} \cr & x = \frac{{27}}{5} \cr & {\text{Average of }}B = 10x \cr & = 10 \times \frac{{27}}{5} \cr & = 54 \cr} $$