A class is divided into two sections A and B . Passing average of 20 students of section A is 80% and passing average of 30 students of section B is 70% . What is the passing average of both the sections ?

Options

A. 0.72
B. 0.74
C. 0.75
D. 0.77

Answer

To find the overall passing average of both sections A and B, we can follow these steps:

### Step 1: Identify the given data
- Section A has 20 students with a passing average of 80%.
- Section B has 30 students with a passing average of 70%.

### Step 2: Calculate the total marks for each section
- For Section A:
\[ \text{Total Marks for A} = \text{Average} \times \text{Number of Students} = 80\% \times 20 = 80 \times 20 = 1600 \]

- For Section B:
\[ \text{Total Marks for B} = \text{Average} \times \text{Number of Students} = 70\% \times 30 = 70 \times 30 = 2100 \]

### Step 3: Calculate the total number of students
\[ \text{Total Students} = \text{Number of Students in A} + \text{Number of Students in B} = 20 + 30 = 50 \]

### Step 4: Calculate the overall average
Using the formula for overall average:
\[ \text{Overall Average} = \frac{\text{Total Marks for A} + \text{Total Marks for B}}{\text{Total Students}} = \frac{1600 + 2100}{50} \]

Calculating the total marks:
\[ \text{Total Marks} = 1600 + 2100 = 3700 \]

Now, substituting back into the average formula:
\[ \text{Overall Average} = \frac{3700}{50} = 74 \]

### Step 5: Convert to percentage
Since we were working with percentages, the overall average is:
\[ \text{Overall Average} = 74\% \]

### Final Answer:
The passing average of both sections A and B is **74%**.

---