Following data depicts the individual and combined score of each of the four students in two different tests - 
UPSC Prelims and UPSC Mains- 
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 1. Abhilash’s score in Prelims is the average of that of Guri & Sandeep in Prelims. 
2. Suketu, who scored 30 marks in prelims got the least of all the 4 aspirants in Prelims exam 
3. Guri, who scored the highest in prelims scored the least in Mains out of the 4 aspirants. His score in Mains 
is equal to 10 
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 4. Sandeep’s score in Mains and prelims are the same. 80 is the highest marks scored by any aspirant across 
Prelims & Mains 
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 5. Abhilash scored a total of 140 marks in UPSC Prelims and Mains combined and is the only aspirant who 
scored more in Mains than Prelims. 
6. Scores of all the aspirants in each of the exams are multiples of 10 and the total scores of Sandeep, Guri & 
Suketu in Prelims and Mains are 100, 50 & 80 not necessarily in the same orde

Let's break down the information given and solve for the scores of each aspirant step by step:

### Information provided:

1. **Abhilash's Prelims score** is the average of Guri and Sandeep's Prelims scores.
2. **Suketu's Prelims score** is 30, which is the least among the four aspirants.
3. **Guri's Prelims score** is the highest, and his **Mains score** is the least (10).
4. **Sandeep's scores** in both Prelims and Mains are the same.
5. **The highest score** in either Prelims or Mains is 80.
6. **Abhilash's total score** (Prelims + Mains) is 140, and he scored more in Mains than in Prelims.
7. All scores are **multiples of 10**.
8. The total scores in **Prelims and Mains** for Sandeep, Guri, and Suketu are **100, 50, and 80**, but not necessarily in that order.

### Solving step by step:

#### 1. Suketu's Prelims and Mains scores:
- **Prelims**: We know Suketu scored 30 in Prelims (as it is the least score).
- **Total (Prelims + Mains)**: From the given total score possibilities (100, 50, 80), Suketu’s total must be 80, because his prelims score (30) is already higher than 50 (one of the other total score options), and Guri has the lowest total.

So, **Suketu's Mains score** = \( 80 - 30 = 50 \).

#### 2. Guri's Prelims and Mains scores:
- **Prelims**: Guri scored the highest in Prelims. The only possible highest score based on the information is 80.
- **Mains**: Guri's Mains score is given as 10.

Thus, **Guri's total score** = \( 80 + 10 = 90 \).

#### 3. Sandeep's Prelims and Mains scores:
- **Prelims = Mains**: It is given that Sandeep scored the same in both Prelims and Mains.
- **Total**: Sandeep’s total score is the remaining total score, 100.
  
Let Sandeep's Prelims and Mains scores both be \( x \). Therefore:
\[
x + x = 100 \quad \Rightarrow \quad 2x = 100 \quad \Rightarrow \quad x = 50
\]
Thus, **Sandeep's Prelims score** = **Sandeep's Mains score** = 50.

#### 4. Abhilash's Prelims and Mains scores:
- **Total**: Abhilash's total score is 140.
- **Prelims and Mains relation**: Abhilash scored more in Mains than in Prelims.
- **Prelims score**: Abhilash's Prelims score is the average of Guri’s and Sandeep’s Prelims scores:
\[
\text{Abhilash's Prelims score} = \frac{80 + 50}{2} = \frac{130}{2} = 65
\]
- **Mains score**: Abhilash’s total score is 140, so:
\[
\text{Abhilash's Mains score} = 140 - 65 = 75
\]

### Final Scores:

1. **Abhilash**: Prelims = 65, Mains = 75, Total = 140
2. **Suketu**: Prelims = 30, Mains = 50, Total = 80
3. **Guri**: Prelims = 80, Mains = 10, Total = 90
4. **Sandeep**: Prelims = 50, Mains = 50, Total = 100

### Conclusion:
The scores for each aspirant in Prelims and Mains are as follows:
- Abhilash: \(65, 75\)
- Suketu: \(30, 50\)
- Guri: \(80, 10\)
- Sandeep: \(50, 50\)

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the average score of all aspirants in the Prelims exam?
2. Who scored the second highest in the Mains exam?
3. What is the combined total of all aspirants' scores in Prelims and Mains?
4. How much more did Guri score in Prelims compared to Mains?
5. If Sandeep’s scores in Mains and Prelims were swapped, how would that affect his total score?

**Tip**: Always double-check each constraint in word problems to ensure that no detail is overlooked.

Following data depicts the individual and combined score of each of the four students in two different tests - UPSC Prelims and UPSC Mains: 1. Abhilash’s score in Prelims is the average of that of Guri & Sandeep in Prelims. 2. Suketu, who scored 30 marks in prelims, got the least of all the 4 aspirants in Prelims exam. 3. Guri, who scored the highest in Prelims, scored the least in Mains out of the 4 aspirants. His score in Mains is equal to 10. 4. Sandeep’s score in Mains and Prelims are the same. 80 is the highest marks scored by any aspirant across Prelims & Mains. 5. Abhilash scored a total of 140 marks in UPSC Prelims and Mains combined and is the only aspirant who scored more in Mains than Prelims. 6. Scores of all the aspirants in each of the exams are multiples of 10 and the total scores of Sandeep, Guri & Suketu in Prelims and Mains are 100, 50 & 80 not necessarily in the same order.

This problem provides a detailed analysis of the individual and combined scores of four aspirants in the UPSC Prelims and Mains. Learn how to calculate scores using averages, logical reasoning, and systems of equations. Suitable for students in Grades 9-12.

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