Question

The ratio of boys to girls in a class is 7 : 5. If there are 48 students in total, the number of girls is:

• A. 18
• B. 20
• C. 22
• D. 24

Hint:

Since the number of girls must correspond to 5 relative parts, the correct option must be a clean multiple of 5! Looking at the choices: 18, 20, 22, and 24, only 20 can be divided evenly by 5. You can pick option (b) instantly without calculating!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A ratio provides a comparative distribution between parts of a whole group. To determine the absolute value of a specific component, we can divide the total group size by the sum of all ratio parts to find the size of a single relative share, and then scale it up by the required component's factor.

Step 2: Key Formula or Approach:
Let the number of boys be $7x$ and the number of girls be $5x$. $$\text{Total Students} = \text{Boys} + \text{Girls}$$ $$\text{Number of Girls} = \left( \frac{\text{Ratio of Girls}}{\text{Sum of Ratios}} \right) \times \text{Total Students}$$

Step 3: Detailed Explanation:
From the problem parameters: Ratio of boys to girls = $7 : 5$ Total students = 48 Calculate the sum of the ratio elements: \[ \text{Total parts} = 7 + 5 = 12 \text{ parts} \] This implies that the 48 students are divided into 12 equal relative components. Let's find the value of 1 relative part ($x$): \[ 12x = 48 \implies x = \frac{48}{12} = 4 \] Now, multiply the size of a single part by the relative ratio value for girls (5 parts) to find the absolute headcount: \[ \text{Number of girls} = 5 \times 4 = 20 \]

Step 4: Final Answer:
The number of girls in the class is 20.