The average marks (out of 100) of boys and girls in an examination are 75 and…
2024
The average marks (out of 100) of boys and girls in an examination are 75 and 80, respectively. If the average marks of all the students in that examination are 78. Find the ratio of the number of boys to the number of girls.
- A.
2 : 3
- B.
3 : 4
- C.
1 : 3
- D.
1 : 2
Attempted by 16 students.
Show answer & explanation
Correct answer: A
Step-by-Step Calculation
Define Variables:
Let B be the number of boys.
Let G be the number of girls.
Average marks of boys = 75.
Average marks of girls = 80.
Overall average marks of all students = 78.
Set up the Weighted Average Equation:
The overall average is the total sum of marks divided by the total number of students:
(75 * B + 80 * G) / (B + G) = 78
Solve the Equation:
Multiply both sides by (B + G):
75B + 80G = 78(B + G)
Expand the right side:
75B + 80G = 78B + 78G
Rearrange the terms to group B and G:
80G - 78G = 78B - 75B
2G = 3B
Find the ratio of boys (B) to girls (G):
B / G = 2 / 3