Question

The ratio of boys to girls in a class is $7:5$. If there are 42 boys, how many girls are there?

• A. 25
• B. 30
• C. 35
• D. 40

Hint:

To solve ratio problems quickly, ask: "What did I multiply the ratio number by to get the real number?" Since $7 \times 6 = 42$, just multiply the other side of the ratio by the same number: $5 \times 6 = 30$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Ratios represent the relative proportion of two quantities.
A ratio of \( 7:5 \) means that for every 7 units of boys, there are 5 units of girls.
Step 2: Key Formula or Approach:
Let the number of boys be \( 7x \) and the number of girls be \( 5x \), where \( x \) is the common multiplier.
Step 3: Detailed Explanation:
Given:
Number of boys = 42.
From the ratio, \( 7x = 42 \).
Solve for \( x \):
\[ x = \frac{42}{7} = 6 \] Now, find the number of girls using the value of \( x \):
\[ \text{Number of girls} = 5x \] \[ \text{Number of girls} = 5 \times 6 = 30 \] Check the total: Boys are 42 and Girls are 30. Ratio = \( 42/30 = 7/5 \). This matches the given condition.
Step 4: Final Answer:
There are 30 girls in the class.