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In a class of 40 students, 45% are girls...

In a class of 40 students, 45% are girls and the remaining are boys. If the average of the girls' marks is 54 and that of the boys is 46, what is the average of the whole class ?

A

`49.7`

B

`49.6`

C

`49.8`

D

`49.5`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these calculations: ### Step 1: Calculate the number of girls in the class. Given that 45% of the class are girls: \[ \text{Number of girls} = 45\% \text{ of } 40 = \frac{45}{100} \times 40 = 18 \] ### Step 2: Calculate the number of boys in the class. Since the total number of students is 40, the number of boys can be calculated as: \[ \text{Number of boys} = 40 - \text{Number of girls} = 40 - 18 = 22 \] ### Step 3: Calculate the total marks of the girls. The average marks of the girls is given as 54. Therefore, the total marks of the girls can be calculated as: \[ \text{Total marks of girls} = \text{Average marks of girls} \times \text{Number of girls} = 54 \times 18 = 972 \] ### Step 4: Calculate the total marks of the boys. The average marks of the boys is given as 46. Therefore, the total marks of the boys can be calculated as: \[ \text{Total marks of boys} = \text{Average marks of boys} \times \text{Number of boys} = 46 \times 22 = 1012 \] ### Step 5: Calculate the total marks of the whole class. The total marks of the whole class is the sum of the total marks of the girls and boys: \[ \text{Total marks of class} = \text{Total marks of girls} + \text{Total marks of boys} = 972 + 1012 = 1984 \] ### Step 6: Calculate the average marks of the whole class. Finally, the average marks of the whole class can be calculated by dividing the total marks by the total number of students: \[ \text{Average marks of class} = \frac{\text{Total marks of class}}{\text{Total number of students}} = \frac{1984}{40} = 49.6 \] ### Final Answer: The average marks of the whole class is **49.6**. ---
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