How many students passed in first class ?
Statements:
I. `85%` of the students who appeared in examination have passed either in first class or in second class.
II. 750 students have passed in seond class.
III. The number of students who passed in first class is `28%` of those passed in second class.

Options

A. All, I , II and III
B. Only I and III
C. Only II and III
D. None of three statements.

Explanation

To determine how many students passed in first class, we will analyze the provided statements step by step.

### Step 1: Understand the Statements
1. **Statement I:** 85% of the students who appeared in the examination have passed either in first class or in second class.
2. **Statement II:** 750 students have passed in second class.
3. **Statement III:** The number of students who passed in first class is 28% of those who passed in second class.

### Step 2: Analyze Statement II
From Statement II, we know that:
- **Number of students who passed in second class = 750.**

### Step 3: Analyze Statement III
From Statement III, we can calculate the number of students who passed in first class:
- **Number of students who passed in first class = 28% of 750.**
- Calculation:
\[ \text{Number of students in first class} = 0.28 \times 750 = 210. \]

### Step 4: Conclusion from Statements II and III
Now that we have calculated the number of students who passed in first class as 210, we can conclude that:
- **The number of students who passed in first class is 210.**

### Step 5: Evaluate Statement I
Statement I states that 85% of students who appeared in the examination passed either in first class or second class. However, this statement does not provide any additional information needed to find the number of students who passed in first class since we already have enough information from Statements II and III.

### Final Conclusion
Thus, we can conclude that to find out how many students passed in first class, only Statements II and III are necessary. Therefore, the answer is:

**The number of students who passed in first class is 210.**

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