Five students Ujith, Mahi, Rizan, Sahir and Amelia appeared for an examination in English and Mathematics .
I. Sahir score more marks than Amelia in Mathematics butscored less in English than Ujith and Mahi
II. In Mathematics Rizan scored more marks than Amelia but less than what Mahi has scored .
III. Amelia scored more than Rizan in English and Rizan scored more than Mahi in English
IV. Ujith scored more than Mahi in Mathematicsbut less than Rizan in English
V. Sahir scored less in Mathematics and top scorer in English are respectively
Which of the following is necessarily correct ?

Options

A. Razan scored more than Sahir in Mathematics
B. Ujith scored more than Sahir both in Mathematics and English
C. Sahir scored more than Ujith in Mathematics
D. Rizan scored more than Ujith both in English and Mathematics

Answer

To solve the problem, we need to analyze the information given step by step and arrange the students according to their scores in Mathematics and English.

### Step 1: Analyze the statements

1. **Sahir scored more marks than Amelia in Mathematics but less in English than Ujith and Mahi.**
- This gives us two pieces of information:
- In Mathematics: Sahir > Amelia
- In English: Sahir < Ujith and Sahir < Mahi

2. **In Mathematics, Rizan scored more marks than Amelia but less than what Mahi has scored.**
- This means:
- In Mathematics: Amelia < Rizan < Mahi

3. **Amelia scored more than Rizan in English and Rizan scored more than Mahi in English.**
- This gives us:
- In English: Rizan < Amelia
- In English: Mahi < Rizan

4. **Ujith scored more than Mahi in Mathematics but less than Rizan in English.**
- This means:
- In Mathematics: Ujith > Mahi
- In English: Rizan > Ujith

5. **Sahir scored less in Mathematics and top scorer in English are respectively.**
- This indicates that Sahir is not the top scorer in either subject.

### Step 2: Organize the information

Now, let's summarize the information we have:

#### Mathematics:
- From statement 1: Sahir > Amelia
- From statement 2: Amelia < Rizan < Mahi
- From statement 4: Ujith > Mahi

Combining these, we can infer:
- Ujith > Mahi > Rizan > Amelia > Sahir

#### English:
- From statement 1: Sahir < Ujith and Sahir < Mahi
- From statement 3: Rizan < Amelia and Mahi < Rizan
- From statement 4: Rizan > Ujith

Combining these, we can infer:
- Amelia > Rizan > Ujith > Mahi > Sahir

### Step 3: Determine the scores

From the above analysis, we can summarize the scores in both subjects:

**Mathematics Ranking:**
1. Ujith
2. Mahi
3. Rizan
4. Amelia
5. Sahir

**English Ranking:**
1. Amelia
2. Rizan
3. Ujith
4. Mahi
5. Sahir

### Conclusion

From the analysis, we can conclude that:
- Ujith is the highest scorer in Mathematics.
- Amelia is the highest scorer in English.

### Final Answer
The necessarily correct statements are:
- Ujith scored more than Mahi in Mathematics.
- Amelia scored more than Rizan in English.