The average mark obtained in a subject by 60 students in a class is 82. The average marks of boys and girls in that subject are 75 and 85 respectively. The number of boys in the class is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 18.
We know that,
Average = Sum of observations/Number of observations
Now,
Total marks of the class = 60 × 82 = 4920
Let the number of boys be x, then the number of girls be (60 - x)
Total marks by boys = 75x
Total marks by girls = 85(60 - x)
⇒ 85(60 - x) + 75x = 4920
⇒ 5100 - 85x + 75x = 4920
⇒ 5100 - 4920 = 85x - 75x
⇒ 180 = 10x
⇒ x = 18
Hence, the number of boys is 18