In a class of 40 students, the ratio of boys to girls is 3:2. The average marks scored by boys is 42, and that by girls is 46. What is the average marks scored by the whole class?
- 43.4
- 43.6
- 43.8
- 44
The Correct Option is B
Approach Solution - 1
To solve the problem, follow these steps:
- Determine the number of boys and girls in the class based on the given ratio: The ratio of boys to girls is 3:2. Let the number of boys be 3x and the number of girls be 2x. Since the total number of students is 40:
3x + 2x = 40
5x = 40
x = 8 - Calculate the number of boys and girls:
Number of boys = 3x = 3(8) = 24
Number of girls = 2x = 2(8) = 16 - Calculate the total marks for boys and girls: The average marks for boys is 42, so the total marks for boys: 42 * 24 = 1008. The average marks for girls is 46, so the total marks for girls: 46 * 16 = 736.
- Determine the average marks for the whole class: The total marks for the entire class is the sum of the total marks for boys and girls:
Total marks for class = 1008 + 736 = 1744
Average marks for the whole class = Total marks for class / Total number of students = 1744 / 40 = 43.6
Therefore, the average marks scored by the whole class is 43.6.
Approach Solution -2
In a class of 40 students, the ratio of boys to girls is 3:2. This means there are \(\frac{3}{5} \times 40 = 24\) boys and \(\frac{2}{5} \times 40 = 16\) girls.
The average marks scored by boys is 42, so the total marks scored by boys is \(24 \times 42 = 1008\).
The average marks scored by girls is 46, so the total marks scored by girls is \(16 \times 46 = 736\).
The total marks scored by the whole class is \(1008 + 736 = 1744\).
The average marks scored by the whole class is \(\frac{1744}{40} = 43.6\).
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