20 children are to be divided into two groups A and B of 12 and 8 children respectively. The average marks obtained by the children of group A is 85 and the average marks of all the 20 children is 80. What is the average marks of children of group B?

Options

A. 72.5
B. 74
C. 78.3
D. 79

Answer

To find the average marks of children in group B, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Marks of All Children:**
- We know the average marks of all 20 children is 80.
- Total marks of all children = Average marks × Number of children
- Total marks = 80 × 20 = 1600.

2. **Calculate the Total Marks of Group A:**
- The average marks of group A (12 children) is 85.
- Total marks of group A = Average marks × Number of children in group A
- Total marks of group A = 85 × 12 = 1020.

3. **Calculate the Total Marks of Group B:**
- Total marks of group B = Total marks of all children - Total marks of group A
- Total marks of group B = 1600 - 1020 = 580.

4. **Calculate the Average Marks of Group B:**
- The number of children in group B is 8.
- Average marks of group B = Total marks of group B ÷ Number of children in group B
- Average marks of group B = 580 ÷ 8 = 72.5.

### Final Answer:
The average marks of children in group B is **72.5**.

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