The average score of 42 students in a test is 69. The ratio of the number of boys to that of girls is 10 : 11. The average score of the boys is 20% more than that of the girls. The average score of the boys is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 75.6
The average score of 42 students in a test is 69.
Now the Sum of scores of all 42 students = Average × total number of students = 42 × 69 = 2898
The ratio of number of Boys to girls = 10 : 11
If boys are 10x then girls will be 11x
⇒ 21x = 42
⇒ x = 2
So,
Number of boys = 20
Number of girls = 22
Let the average score of girls = y
So,
The average score of boys = y + y × 20/100 = 6y/5
Sum of scores of all 42 students = 22y + 20 × (6y/5) = 46y
⇒ 46y = 2898
⇒ y = 63
So, the average score of boys = (6 × 63/5) = 75.6