Average marks of 15 students ofclassfirst is 160. Avearge marks of 10 students ofclass second is 120. Average marks of 15 students of class third is 180. What will be the average marks of students of all the classes together?

Options

A. 157.5
B. 162.5
C. 155.5
D. 167.5

Answer

To find the average marks of students of all classes together, we need to follow these steps:

### Step 1: Calculate the total marks for each class.
1. **Class 1**:
- Average marks = 160
- Number of students = 15
- Total marks = Average marks × Number of students = 160 × 15 = 2400

2. **Class 2**:
- Average marks = 120
- Number of students = 10
- Total marks = Average marks × Number of students = 120 × 10 = 1200

3. **Class 3**:
- Average marks = 180
- Number of students = 15
- Total marks = Average marks × Number of students = 180 × 15 = 2700

### Step 2: Calculate the total marks of all classes combined.
- Total marks of all classes = Total marks of Class 1 + Total marks of Class 2 + Total marks of Class 3
- Total marks = 2400 + 1200 + 2700 = 6300

### Step 3: Calculate the total number of students.
- Total number of students = Number of students in Class 1 + Number of students in Class 2 + Number of students in Class 3
- Total students = 15 + 10 + 15 = 40

### Step 4: Calculate the average marks of all students combined.
- Average marks = Total marks of all classes / Total number of students
- Average marks = 6300 / 40 = 157.5

Thus, the average marks of students of all classes together is **157.5**.