The ratio of boys and girls in a class is `5:3.20%` of the boys and `60%` of the girls have passed in first class. What percentage of the class has passed in first class ?

Options

A. `35%`
B. `32%`
C. `34%`
D. `33%`

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Define the Variables
Let the common multiple for the ratio of boys and girls be \( x \). According to the ratio given, the number of boys is \( 5x \) and the number of girls is \( 3x \).

### Step 2: Calculate the Total Number of Students
The total number of students in the class can be calculated as follows:
\[ \text{Total Students} = \text{Number of Boys} + \text{Number of Girls} = 5x + 3x = 8x \]

### Step 3: Calculate the Number of Boys Who Passed
We know that 20% of the boys passed in the first class. Therefore, the number of boys who passed is:
\[ \text{Boys Passed} = 20\% \text{ of } 5x = \frac{20}{100} \times 5x = \frac{1}{5} \times 5x = x \]

### Step 4: Calculate the Number of Girls Who Passed
Similarly, 60% of the girls passed in the first class. Therefore, the number of girls who passed is:
\[ \text{Girls Passed} = 60\% \text{ of } 3x = \frac{60}{100} \times 3x = \frac{3}{5} \times 3x = \frac{9}{5}x \]

### Step 5: Calculate the Total Number of Students Who Passed
Now, we can find the total number of students who passed in the first class:
\[ \text{Total Passed} = \text{Boys Passed} + \text{Girls Passed} = x + \frac{9}{5}x \]
To add these, we convert \( x \) into a fraction with a common denominator:
\[ x = \frac{5}{5}x \]
Thus,
\[ \text{Total Passed} = \frac{5}{5}x + \frac{9}{5}x = \frac{14}{5}x \]

### Step 6: Calculate the Percentage of the Class That Passed
To find the percentage of the class that passed in the first class, we use the formula:
\[ \text{Percentage Passed} = \left( \frac{\text{Total Passed}}{\text{Total Students}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Passed} = \left( \frac{\frac{14}{5}x}{8x} \right) \times 100 \]
The \( x \) cancels out:
\[ = \left( \frac{14}{5 \times 8} \right) \times 100 = \left( \frac{14}{40} \right) \times 100 = \frac{14 \times 100}{40} = \frac{1400}{40} = 35\% \]

### Final Answer
Therefore, the percentage of the class that has passed in the first class is **35%**.

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