The average score in Mathematics of 90 students of section A and B of class IX was 63. The number of students in A were 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:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 54
Let the students in section B be ‘x’
Students in section A = x + 10
Number of the students = 90
x + x + 10 = 90
x = 40
Students in Section B = 40
Students in section A = 50
Total score of students = 90 x 63 = 5670
Let the average be ‘k’.
Average of students in section A = 130% of students in section B
Let the average of students in Section B = 10K
Sum of score of students in Section B = 10K x 40 = 400K
Therefore, the average of students in Section A = 13K
Sum of score of students in Section B = 13K x 50 = 650
According to question
⇒ 650K + 400K = 5670
⇒ 1050K = 5670
⇒ K = 5.4
Average of students in section B = 10K
⇒ 5.4 × 10
⇒ 54
Using Alligation
Using Alligation formula
13K × 5 + 10K × 4 = 63 (4 + 5)
Upon solving
K = 5.4
Average of students in Section B = 5.4 x 10 = 54