The average marks of three batches of students containing 70,50 and 30 students respectively, are 50,55 and 45. Find the average marks of all the 150 students.

Answer

To find the average marks of all 150 students from three batches, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of students and their average marks in each batch:**
- Batch 1: 70 students with an average of 50 marks.
- Batch 2: 50 students with an average of 55 marks.
- Batch 3: 30 students with an average of 45 marks.

2. **Calculate the total marks for each batch:**
- For Batch 1:
\[ \text{Total Marks}_1 = \text{Number of Students}_1 \times \text{Average Marks}_1 = 70 \times 50 = 3500 \]
- For Batch 2:
\[ \text{Total Marks}_2 = \text{Number of Students}_2 \times \text{Average Marks}_2 = 50 \times 55 = 2750 \]
- For Batch 3:
\[ \text{Total Marks}_3 = \text{Number of Students}_3 \times \text{Average Marks}_3 = 30 \times 45 = 1350 \]

3. **Sum the total marks from all batches:**
\[ \text{Total Marks} = \text{Total Marks}_1 + \text{Total Marks}_2 + \text{Total Marks}_3 = 3500 + 2750 + 1350 = 7600 \]

4. **Calculate the total number of students:**
\[ \text{Total Students} = 70 + 50 + 30 = 150 \]

5. **Find the average marks of all students:**
\[ \text{Average Marks} = \frac{\text{Total Marks}}{\text{Total Students}} = \frac{7600}{150} \]
- Simplifying this gives:
\[ \text{Average Marks} = 50.67 \text{ (approximately)} \]

### Final Answer:
The average marks of all 150 students is approximately **50.67**.