A student obtained 62 and 48 marks in the first and secound examinations of class XI. Find the minimum marks he should get in annul examination to have an average of at least 60 marks.

Explanation

To solve the problem step by step, we need to find the minimum marks a student should obtain in the annual examination to achieve an average of at least 60 marks across three examinations.

### Step-by-Step Solution:

1. **Identify the Marks from Previous Examinations**:
- Marks in the first examination = 62
- Marks in the second examination = 48

2. **Let x be the Marks in the Annual Examination**:
- We need to find the value of x.

3. **Set Up the Average Formula**:
- The average of the three examinations can be calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of all marks}}{\text{Number of examinations}} \]
- For our case, this becomes:
\[ \text{Average} = \frac{62 + 48 + x}{3} \]

4. **Set Up the Inequality for the Average**:
- We want the average to be at least 60:
\[ \frac{62 + 48 + x}{3} \geq 60 \]

5. **Multiply Both Sides by 3**:
- To eliminate the fraction, multiply both sides by 3:
\[ 62 + 48 + x \geq 180 \]

6. **Calculate the Left Side**:
- Combine the known marks:
\[ 110 + x \geq 180 \]

7. **Isolate x**:
- Subtract 110 from both sides:
\[ x \geq 180 - 110 \]
\[ x \geq 70 \]

8. **Conclusion**:
- The minimum marks the student should obtain in the annual examination is:
\[ \text{Minimum marks} = 70 \]

### Final Answer:
The student must score at least 70 marks in the annual examination.

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