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

Answer

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

### Step-by-Step Solution:

1. **Identify the number of students and their average marks for each batch:**
- Batch A: 55 students with an average of 50 marks.
- Batch B: 60 students with an average of 55 marks.
- Batch C: 45 students with an average of 60 marks.

2. **Calculate the total marks for each batch:**
- For Batch A:
\[ \text{Total Marks for Batch A} = \text{Average} \times \text{Number of Students} = 50 \times 55 = 2750 \]
- For Batch B:
\[ \text{Total Marks for Batch B} = \text{Average} \times \text{Number of Students} = 55 \times 60 = 3300 \]
- For Batch C:
\[ \text{Total Marks for Batch C} = \text{Average} \times \text{Number of Students} = 60 \times 45 = 2700 \]

3. **Calculate the total marks of all students combined:**
\[ \text{Total Marks} = \text{Total Marks for Batch A} + \text{Total Marks for Batch B} + \text{Total Marks for Batch C} \]
\[ \text{Total Marks} = 2750 + 3300 + 2700 = 8750 \]

4. **Calculate the total number of students:**
\[ \text{Total Number of Students} = 55 + 60 + 45 = 160 \]

5. **Calculate the average marks of all students:**
\[ \text{Average Marks} = \frac{\text{Total Marks}}{\text{Total Number of Students}} = \frac{8750}{160} \]
\[ \text{Average Marks} = 54.6875 \]

### Final Answer:
The average marks of all the students combined is **54.6875**.