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In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class?
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In a class of 40 students, the girls outnumber the boys. In a test whe...
Given Information:
- Total number of students = 40
- Girls outnumber boys
- Maximum marks = 170
- Average marks scored by girls = 150
- Average marks scored by boys = 130
- All boys have different consecutive integer marks
- Average marks of top 9 boys = 133
Calculating the number of girls and boys:
Let's assume there are 'g' girls and 'b' boys in the class. We know that girls outnumber boys, so 'g' > 'b'.
Since the total number of students is 40, we can write an equation:
g + b = 40
Calculating the average marks of the whole class:
To calculate the average marks of the whole class, we need to find the sum of the marks of all the students.
The sum of the marks of the girls can be calculated using the average marks and the number of girls:
Sum of girls' marks = Average marks of girls * Number of girls = 150 * g
The sum of the marks of the boys can be calculated using the average marks and the number of boys:
Sum of boys' marks = Average marks of boys * Number of boys = 130 * b
The sum of the marks of all the students can be calculated by adding the sums of the marks of the girls and boys:
Sum of all students' marks = Sum of girls' marks + Sum of boys' marks
Calculating the number of boys:
From the given information, we know that the average marks of the top 9 boys is 133. This means that the sum of their marks is:
Sum of top 9 boys' marks = Average marks of top 9 boys * Number of top 9 boys = 133 * 9
We also know that all the boys have different consecutive integer marks. This means that the sum of the marks of the top 9 boys can be calculated using the formula for the sum of an arithmetic series:
Sum of top 9 boys' marks = (First boy's marks + Last boy's marks) * Number of top 9 boys / 2
Since the marks are consecutive integers, the first boy's marks would be the lowest mark, and the last boy's marks would be the highest mark. Therefore, we can write an equation:
(First boy's marks + Last boy's marks) * Number of top 9 boys / 2 = Sum of top 9 boys' marks
Using this equation, we can calculate the number of top 9 boys.
Substituting the values and calculating the average marks of the whole class:
Now, we have all the necessary information to calculate the average marks of the whole class.
From the equation g + b = 40, we can substitute the value of b with the calculated value of the number of top 9 boys to get the number of girls.
We can then substitute the values of g and b in the equation Sum of all students' marks = Sum of girls' marks + Sum of boys' marks to get the sum of all the students' marks.
Finally, we can calculate the average marks of the whole class by dividing the sum of all students' marks by the total number of students (40).
This will give us the average marks of the whole class.
- Total number of students = 40
- Girls outnumber boys
- Maximum marks = 170
- Average marks scored by girls = 150
- Average marks scored by boys = 130
- All boys have different consecutive integer marks
- Average marks of top 9 boys = 133
Calculating the number of girls and boys:
Let's assume there are 'g' girls and 'b' boys in the class. We know that girls outnumber boys, so 'g' > 'b'.
Since the total number of students is 40, we can write an equation:
g + b = 40
Calculating the average marks of the whole class:
To calculate the average marks of the whole class, we need to find the sum of the marks of all the students.
The sum of the marks of the girls can be calculated using the average marks and the number of girls:
Sum of girls' marks = Average marks of girls * Number of girls = 150 * g
The sum of the marks of the boys can be calculated using the average marks and the number of boys:
Sum of boys' marks = Average marks of boys * Number of boys = 130 * b
The sum of the marks of all the students can be calculated by adding the sums of the marks of the girls and boys:
Sum of all students' marks = Sum of girls' marks + Sum of boys' marks
Calculating the number of boys:
From the given information, we know that the average marks of the top 9 boys is 133. This means that the sum of their marks is:
Sum of top 9 boys' marks = Average marks of top 9 boys * Number of top 9 boys = 133 * 9
We also know that all the boys have different consecutive integer marks. This means that the sum of the marks of the top 9 boys can be calculated using the formula for the sum of an arithmetic series:
Sum of top 9 boys' marks = (First boy's marks + Last boy's marks) * Number of top 9 boys / 2
Since the marks are consecutive integers, the first boy's marks would be the lowest mark, and the last boy's marks would be the highest mark. Therefore, we can write an equation:
(First boy's marks + Last boy's marks) * Number of top 9 boys / 2 = Sum of top 9 boys' marks
Using this equation, we can calculate the number of top 9 boys.
Substituting the values and calculating the average marks of the whole class:
Now, we have all the necessary information to calculate the average marks of the whole class.
From the equation g + b = 40, we can substitute the value of b with the calculated value of the number of top 9 boys to get the number of girls.
We can then substitute the values of g and b in the equation Sum of all students' marks = Sum of girls' marks + Sum of boys' marks to get the sum of all the students' marks.
Finally, we can calculate the average marks of the whole class by dividing the sum of all students' marks by the total number of students (40).
This will give us the average marks of the whole class.
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In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class?
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In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class?.
In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class?.
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In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class?, a detailed solution for In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? has been provided alongside types of In a class of 40 students, the girls outnumber the boys. In a test where the maximum marks are 170, the average marks scored by girls is 150, and that by boys is 130. The marks of all the boys are different consecutive integers. If the average marks scored by the top 9 boys is 133, what were the average marks of the whole class? theory, EduRev gives you an
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