Question

In an exam, the ratio of boys to girls is 3:2. If 20% of the boys and 30% of the girls fail, what is the overall percentage of students who fail?

• A. 24%
• B. 25%
• C. 26%
• D. 27%

Hint:

Use a common base (like 100) when solving ratio-based percentage questions for accuracy and simplicity.

Answer 1

The Correct Option is A

To solve the problem, we need to find the overall percentage of students who fail, based on the failure rates among boys and girls and their ratio in the class.

1. Understanding the Concepts:

- Ratio: Represents a comparative value. A ratio of 3:2 means for every 3 boys, there are 2 girls.
- Percentage: A way to express a number as a part of a whole (out of 100).
- Weighted Average: Since the numbers of boys and girls are different, we need a weighted average failure rate based on their ratio.

2. Given Values:

Ratio of boys to girls = 3 : 2
Let total students = 3 + 2 = 5 parts
Assume total students = 100 (for easier calculation; you can also work in ratios). Then,
Boys = 60 (i.e., 3 parts out of 5 ⇒ 3/5 × 100 = 60)
Girls = 40 (i.e., 2 parts out of 5 ⇒ 2/5 × 100 = 40)
Failing Boys = 20% of 60 = 12
Failing Girls = 30% of 40 = 12

3. Calculating Overall Percentage of Failures:

Total failing students = 12 (boys) + 12 (girls) = 24
Total students = 100

\[ \text{Overall Failure Percentage} = \frac{24}{100} \times 100 = 24\% \]

Final Answer:

The overall percentage of students who fail is 24%.

Answer 2

To solve the problem of determining the overall percentage of students who fail, we need to break it down step-by-step:

First, let's define the variables:
Ratio of boys to girls: 3:2. This implies that, for every 5 students, 3 are boys and 2 are girls.

Total students: We can assume the total number of students is \(5n\), where \(n\) is a common multiple.

Therefore, the number of boys is \(3n\) and the number of girls is \(2n\).

Fail percentages: 20% of boys and 30% of girls fail.

Now, calculate the number of boys and girls who fail:
Boys failing: \(0.2 \times 3n = 0.6n\)
Girls failing: \(0.3 \times 2n = 0.6n\)

Total students failing: \(0.6n + 0.6n = 1.2n\)

The total number of students is \(5n\), so the percentage of students who fail is:

\[\text{Percentage failing} = \left(\frac{1.2n}{5n}\right) \times 100\]

\[\text{Percentage failing} = \left(\frac{1.2}{5}\right) \times 100 = 0.24 \times 100 = 24\%\]

Thus, the overall percentage of students failing the exam is 24%.