Question

The average marks of boys in a class is $52$ and that of girls is $42$. The average marks of boys and girls combined are $50$. The percentage of boys in the class is:

• A. $40\%$
• B. $20\%$
• C. $80\%$
• D. $60\%$

Answer 1

The correct option is C

$80\%$

Explanation for the correct option:

Calculating the percentage of boys in the class:

Step 1: Finding the total marks of boys and girls

Let the number of boys be $x$ and number of girls be $y$.

Total marks obtained by all the boys

$$\begin{gathered} =\text{average marks}\times \text{number of boys} \\ =52x \end{gathered}$$

Total marks obtained by all the girls

$$\begin{gathered} =\text{average marks}\times \text{number of gilrs} \\ =42y \end{gathered}$$

Step 2: Finding average marks of boys and girls together

The average marks of boys and girls combined is:

$$\begin{gathered} =\frac{\text{Total marks obtained by boys + Total marks obtained by girls}}{\text{Number of boys + Number of girls}} \\ =\frac{52x+42y}{x+y} \\ \Rightarrow \frac{52x+42y}{x+y}=50\left[\text{Given}\right] \\ \Rightarrow 52x+42y=50x+50y \\ \Rightarrow 2x=8y \\ \Rightarrow x=4y \end{gathered}$$

Therefore, the ratio of boys to girls is $4:1$

Step 3: Finding the percentage of boys in class

Hence, the percentage of boys in the class is:

$$\begin{gathered} =\frac{4}{5}\times 100 \\ =80\% \end{gathered}$$

Thus, option (C) is the correct answer.