The average score in Mathematics of 90 students of section A and B of class IX was 63. The number of students in A was 10 more than those in B. The average score of students in A was 30% more than that of students in B. The average score of students in B is:
Answer & explanation
Correct answer: option 2
Difference of no. of students = 10
Hence, no. of students in A = 50 and B = 40
Ratio of No. of students ⇒ A : B = 5 : 4
30% = +\(\frac{3}{10}\)
Ratio of average score ⇒ A : B = 13 : 10
Now,
Accordingly average of (A + B) = \(\frac{(13 × 5) + (10 × 4)}{5 + 4}\) = \(\frac{105}{9}\) = \(\frac{35}{3}\)
ATQ,
\(\frac{35}{3}\)R = 63
1R = 63 × \(\frac{3}{35}\)
Average score of B = 10R = 10× 63 × \(\frac{3}{35}\) = 54