In a class, the average score of girls in an examination is 73 and that of boys is 71. The average score for the whole class Is 71.8. Find the percentage of girls.

Options

A. 0.4
B. 0.5
C. 0.55
D. 0.6

Answer

To solve the problem, we need to find the percentage of girls in the class based on the average scores provided. Let's denote:

- \( G \) = number of girls
- \( B \) = number of boys
- \( A_g \) = average score of girls = 73
- \( A_b \) = average score of boys = 71
- \( A \) = average score of the whole class = 71.8

We can use the formula for the average score of the entire class, which is given by:

\[ A = \frac{A_g \cdot G + A_b \cdot B}{G + B} \]

Substituting the known values into the formula, we get:

\[ 71.8 = \frac{73G + 71B}{G + B} \]

Now, we can cross-multiply to eliminate the fraction:

\[ 71.8(G + B) = 73G + 71B \]

Expanding both sides gives:

\[ 71.8G + 71.8B = 73G + 71B \]

Now, we can rearrange the equation to isolate terms involving \( G \) and \( B \):

\[ 71.8G + 71.8B - 71B = 73G \]

This simplifies to:

\[ 71.8G + 0.8B = 73G \]

Now, we can move \( 71.8G \) to the right side:

\[ 0.8B = 73G - 71.8G \]

This simplifies to:

\[ 0.8B = 1.2G \]

Next, we can express \( B \) in terms of \( G \):

\[ B = \frac{1.2G}{0.8} = 1.5G \]

Now, we can find the total number of students in the class:

\[ G + B = G + 1.5G = 2.5G \]

To find the percentage of girls in the class, we use the formula:

\[ \text{Percentage of girls} = \frac{G}{G + B} \times 100 \]

Substituting \( G + B = 2.5G \):

\[ \text{Percentage of girls} = \frac{G}{2.5G} \times 100 = \frac{1}{2.5} \times 100 = 40\% \]

Thus, the percentage of girls in the class is **40%**.