If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is

Options

A. 54.68
B. 53.33
C. 55
D. None of these

Answer

To find the average marks of all the students from the three batches, we can follow these steps:

### Step 1: Calculate the total marks for each batch
1. **Batch 1**:
- Number of students = 55
- Average marks = 50
- Total marks = Number of students × Average marks = 55 × 50 = 2750

2. **Batch 2**:
- Number of students = 60
- Average marks = 55
- Total marks = Number of students × Average marks = 60 × 55 = 3300

3. **Batch 3**:
- Number of students = 45
- Average marks = 60
- Total marks = Number of students × Average marks = 45 × 60 = 2700

### Step 2: Calculate the total marks for all batches
- Total marks from all batches = Total marks from Batch 1 + Total marks from Batch 2 + Total marks from Batch 3
- Total marks = 2750 + 3300 + 2700 = 8750

### Step 3: Calculate the total number of students
- Total number of students = Number of students in Batch 1 + Number of students in Batch 2 + Number of students in Batch 3
- Total students = 55 + 60 + 45 = 160

### Step 4: Calculate the average marks of all students
- Average marks = Total marks / Total number of students
- Average marks = 8750 / 160 = 54.6875

### Final Answer
The average marks of all the students is approximately **54.69**.

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