The average marks scored by the students of a class is 75. If the average marks scored by the girls in the same class is 90 and that of boys is 70, what is the percentage of boys in the class?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 75%.
The total number of students in the class be 'T'.
The number of boys in the class be 'B'.
The number of girls in the class be 'G'.
Total average marks = (Total marks of boys + Total marks of girls) / Total students
⇒ 75 = (70B + 90G) / T
⇒ T = B + G
⇒ 75T = 70B + 90G
⇒ 75(B + G) = 70B + 90G
⇒ 75B + 75G = 70B + 90G
⇒ 5B = 15G
⇒ B/G = 3/1
⇒ Percentage of boys = (Number of boys / Total students) × 100
⇒ Percentage of boys = (B / (B + G)) × 100
⇒ Percentage of boys = (3 / (3 + 1)) × 100
⇒ Percentage of boys = (3/4) × 100
⇒ Percentage of boys = 75%
Therefore, the percentage of boys in the class is 75%.