The average marks scored by 3 students was 71 if another student's marks was considered the average marks of four students became 74 how many marks did the 4th student score?

Options

A. 86
B. 83
C. 87
D. 80

Answer

To solve the problem step by step, we can follow these calculations:

1. **Understanding the Average Marks of Three Students**:
- We know that the average marks of three students is 71.
- The formula for average is given by:
\[ \text{Average} = \frac{\text{Total Marks}}{\text{Number of Students}} \]
- Therefore, the total marks scored by the three students can be calculated as:
\[ \text{Total Marks of 3 students} = \text{Average} \times \text{Number of Students} = 71 \times 3 = 213 \]

2. **Understanding the Average Marks of Four Students**:
- When a fourth student is included, the average marks of the four students becomes 74.
- Using the same formula for average, we can calculate the total marks scored by the four students:
\[ \text{Total Marks of 4 students} = \text{Average} \times \text{Number of Students} = 74 \times 4 = 296 \]

3. **Finding the Marks of the Fourth Student**:
- We need to find out how many marks the fourth student scored. Let's denote the marks of the fourth student as \( x \).
- According to the information we have:
\[ \text{Total Marks of 4 students} = \text{Total Marks of 3 students} + \text{Marks of 4th student} \]
- Substituting the values we calculated:
\[ 296 = 213 + x \]
- To find \( x \), we can rearrange the equation:
\[ x = 296 - 213 = 83 \]

4. **Conclusion**:
- Therefore, the marks scored by the fourth student is \( \boxed{83} \).