Step 1: Understanding the Concept:
A ratio is a way to compare two quantities of the same kind by division.
The ratio 5 : 3 indicates that for every 5 units of boys, there are 3 units of girls in the class.
We can treat these "units" as a common multiplier \( x \), making the actual numbers \( 5x \) and \( 3x \).
Key Formula or Approach:
If the ratio of A to B is \( a : b \), and the value of A is given, we can find the value of B using:
\[ B = \frac{\text{Value of A} \times b}{a} \]
Or by finding the value of one "unit" first.
Step 2: Detailed Explanation:
Let the number of boys be \( 5x \) and the number of girls be \( 3x \).
The problem states that the actual number of boys is 40.
So, we set up an equation:
\[ 5x = 40 \]
To find the value of \( x \) (the value per unit), divide both sides by 5:
\[ x = \frac{40}{5} \]
\[ x = 8 \]
Now that we know one unit represents 8 individuals, we can find the number of girls.
The number of girls is represented by \( 3x \).
Substitute \( x = 8 \) into this expression:
\[ \text{Number of girls} = 3 \times 8 \]
\[ \text{Number of girls} = 24 \]
We can double-check the ratio:
Ratio = \(\frac{\text{Boys}}{\text{Girls}} = \frac{40}{24}\).
Divide both numerator and denominator by their HCF (which is 8):
\[ \frac{40 \div 8}{24 \div 8} = \frac{5}{3} \]
The calculated values correctly satisfy the given ratio.
Step 3: Final Answer:
There are 24 girls in the class.
This matches Option (B).