Question

What is Akhil's score on Day 1?

• A. 6
• B. 7
• C. 5
• D. 8
• A. Cannot be determined
• B. Akhil
• C. Bimal
• D. Chatur
• A. 4
• B. 5
• C. 6
• D. Cannot be determined

Answer 1

The Correct Option is B

To solve the problem and find Akhil's score on Day 1, we should analyze the given data and logical conditions:

1. The 2-day average for Day 2 is 15. Thus, the equation for Day 1 and Day 2's total score is:
   $$ \text{Total Day 1} + \text{Total Day 2} = 2 \times 15 = 30 $$
   The 2-day average for Day 3 is 15.5. Thus, the equation for Day 2 and Day 3's total score is:
   $$ \text{Total Day 2} + \text{Total Day 3} = 2 \times 15.5 = 31 $$
   The 2-day average for Day 4 is 16. Thus, the equation for Day 3 and Day 4's total score is:
   $$ \text{Total Day 3} + \text{Total Day 4} = 2 \times 16 = 32 $$
   The 2-day average for Day 5 is 17. Thus, the equation for Day 4 and Day 5's total score is:
   $$ \text{Total Day 4} + \text{Total Day 5} = 2 \times 17 = 34 $$
   Total scores of Days 3 and 4 are equal, so:
   $$ \text{Total Day 3} = \text{Total Day 4} = 16 $$
2. Now, we have:
   $$ \text{Total Day 2} + 16 = 31 \Rightarrow \text{Total Day 2} = 15 $$
   Substituting into first equation for Day 1 & Day 2:
   $$ \text{Total Day 1} + 15 = 30 \Rightarrow \text{Total Day 1} = 15 $$
   So, Total Day 1's score is 15.
3. Participants' ranks for Day 1 are:
   
   • Akhil: 1
   • Bimal: 2
   • Chatur: 3
   Chatur's score must be lowest (multiple of 3); possible scores: 3, 6, or 9. It's given Chatur's minimum, matching Akhil’s score on Day 4 (3).
4. Akhil's rank is 1, he has the highest score on Day 1:
5. The scores can be distributed considering conditions:

   Participants	Score
   Akhil	7
   Bimal	5
   Chatur	3

   Thus, Akhil's score on Day 1 is 7.

Answer 2

To solve the problem of determining who attains the maximum total score, we must analyze the information and utilize logical reasoning based on the constraints and data provided. 

Given:
- 2-day averages from Day 2 to Day 5.
- Ranks for each day.
- Specific constraints about the participants' scores.

Let's calculate the total scores for Days 1 through 5:

Day	Total Score
Day 1	x
Day 2	y
Day 3	z
Day 4	z
Day 5	a

From the 2-day averages:

• (x + y) / 2 = 15 ⟹ x + y = 30
• (y + z) / 2 = 15.5 ⟹ y + z = 31
• (z + z) / 2 = 16 ⟹ z = 16
• (z + a) / 2 = 17 ⟹ a = 18

Solving these:

• z = 16
• y + 16 = 31 ⟹ y = 15
• x + 15 = 30 ⟹ x = 15
• z + a = 34 ⟹ a = 18

Total scores per day:

• Day 1: 15
• Day 2: 15
• Day 3: 16
• Day 4: 16
• Day 5: 18

Given Rank Constraints:

• Chatur’s score is always a multiple of 3
• Lowest score on Day 1 (equal to Akhil’s score on Day 4)
• Highest unique score on Day 2

Chatur’s Scores:

• Day 1: 6 (same as Akhil’s Day 4 score)
• Day 2: 9 (unique and highest)
• Day 3: 6
• Day 4: 6
• Day 5: 12

Bimal’s Scores:

• Day 1: 5
• Day 2: 4
• Day 3: 5
• Day 4: 7
• Day 5: 7
• Total: 28

Akhil’s Scores:

• Day 1: 4
• Day 2: 2
• Day 3: 5
• Day 4: 3
• Day 5: 5
• Total: 19

Chatur’s Total Score: 6 + 9 + 6 + 6 + 12 = 39

Conclusion: Chatur attains the maximum total score.

Answer 3

Let's consider the following table for minimum possible total score of Bimal:  

 

	Day 1	Day 2	Day 3	Day 4	Day 5	Total Score
Akhil	7	\(\frac{4}{5}\)	5	3	\(\frac{5}{4}\)	23 / 24 / 25
Bimal	5	\(\frac{2}{1}\)	5	7	\(\frac{7}{8}\)	27 / 26 / 25
Chatur	3	9	6	6	6	30
Total score	15	15	16	16	18	80

From the table, we can see that the minimum score obtained by Bimal is 25.

So, the correct answer is: 25.

Answer 4

Let's see the final table of total scores of Bimal: 

	Day 1	Day 2	Day 3	Day 4	Day 5	Total Score
Akhil	7	\(\frac{4}{5}\)	5	3	\(\frac{5}{4}\)	23 / 24 / 25
Bimal	5	\(\frac{2}{1}\)	5	7	\(\frac{7}{8}\)	27 / 26 / 25
Chatur	3	9	6	6	6	30
Total Score	15	15	16	16	18	80

The question says that Bimal's total score is a multiple of 3, which means his total score is 27.
This means Akhil's total score is 23.
Akhil scores 23 when his scores on Days 1, 2, 3, 4, and 5 are 7, 4, 5, 3, and 4.
So, Akhil's score on Day 2 is 4.

Answer 5

Bimal's Total Score 

To determine Bimal's total score given Akhil's total score of 24, let's analyze the data step-by-step:

2-Day Averages:

• Day 2: \(15\)
• Day 3: \(15.5\)
• Day 4: \(16\)
• Day 5: \(17\)

Let the total scores for each day be:

• Day 1: \(x\)
• Day 2: \(y\)
• Day 3 and Day 4: \(z\)
• Day 5: \(w\)

Using the average equations:

• \(\frac{x + y}{2} = 15 \Rightarrow x + y = 30\)
• \(\frac{y + z}{2} = 15.5 \Rightarrow y + z = 31\)
• \(\frac{z + z}{2} = 16 \Rightarrow z = 16\)
• \(\frac{z + w}{2} = 17 \Rightarrow w = 18\)
• \(y = 15\), \(x = 15\)

So, total scores per day:

• Day 1: \(15\)
• Day 2: \(15\)
• Day 3: \(16\)
• Day 4: \(16\)
• Day 5: \(18\)

Participants’ Scores

• Chatur: Always multiples of 3
• Chatur's highest score is on Day 2 (unique highest)
• Lowest score on Day 1 equals Akhil's score on Day 4 (\(= 3\))

Assigning scores:

• Day 1: Chatur = 3, Akhil = 7 (rank 1), Bimal = 5
• Day 2: Chatur = 9, Akhil = 4 (rank 2), Bimal = 2 (rank 3)
• Day 3: Chatur = 6, Akhil = 5, Bimal = 5
• Day 4: Chatur = 6, Akhil = 3, Bimal = 7
• Day 5: Chatur = 9, Akhil = 4, Bimal = 5

Total Scores:

• Akhil: \(7 + 4 + 5 + 3 + 5 = 24\)
• Bimal: \(5 + 2 + 5 + 7 + 7 = 26\)
• Chatur: \(3 + 9 + 6 + 6 + 9 = 33\)

Therefore, Bimal's total score is: 26