Question

If the ratio of boys to girls in a class is 7 : 5 and the total number of students is 48, then 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 whole multiple of 5! Looking at the choices: 18, 20, 22, and 24, only 20 can be cleanly divided by 5. You can confidently select option (b) in a matter of seconds.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Ratios provide a way to compare quantities of the same kind. A ratio of 7 : 5 implies that for every group of 12 students (7+5), 7 are boys and 5 are girls.
To find the actual quantity from a ratio, we assume a common multiplier (variable) \(x\) that represents the value of one "part" or "unit" of the ratio.
The total population is the sum of these parts. By finding the value of \(x\), we can find the individual counts of boys and girls.
Step 2: Key Formula or Approach:
1. Let Boys = \(7x\) and Girls = \(5x\)
2. Total Students = Boys + Girls
3. Number of Girls = \( \frac{\text{Ratio of Girls}}{\text{Sum of Ratios}} \times \text{Total Count} \)
Step 3: Detailed Explanation:
Given Parameters:
Ratio (Boys : Girls) = 7 : 5
Total Students = 48
Let us represent the categories algebraically:
Number of boys = \(7x\)
Number of girls = \(5x\)
Summing these up gives the total class strength:
\[ 7x + 5x = 48 \]
\[ 12x = 48 \]
Isolating \(x\) to find the value of one ratio unit:
\[ x = \frac{48}{12} \]
\[ x = 4 \]
Now that we know one part is equal to 4 students, we calculate the number of girls by multiplying the girl's ratio share by the unit value:
\[ \text{Number of Girls} = 5 \times x \]
\[ \text{Number of Girls} = 5 \times 4 \]
\[ \text{Number of Girls} = 20 \]
For verification:
Number of Boys = \( 7 \times 4 = 28 \)
Total = \( 28 + 20 = 48 \). This confirms the solution is correct.
Step 4: Final Answer:
The total number of girls in the class is 20.