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.
Correct Answer :
2 : 3
Solution :
The correct option is 2 : 3.
To find the ratio of the number of boys to the number of girls, we can set up an algebraic equation using the given averages.
Let the number of boys be and the number of girls be .
According to the problem:
The average marks of the boys is 75. Therefore, the total marks scored by the boys is:
The average marks of the girls is 80. Therefore, the total marks scored by the girls is:
The total marks scored by all the students combined is:
We are also given that the average marks of all students is 78. Since the total number of students is , the total marks scored by all students can also be expressed as:
Now, we equate the two expressions for the total marks:
Next, we expand the right side of the equation:
Rearranging the terms to group the terms on one side and the terms on the other side:
Simplifying both sides:
To find the ratio of the number of boys to the number of girls (), we divide both sides by and then by 3:
Therefore, the ratio of the number of boys to the number of girls is 2 : 3.
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