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 determine Akhil's Day 1 score, the provided data and conditions are analyzed:

1. The following equations are derived from the 2-day averages: Day 1 + Day 2 = 2 * 15 = 30 Day 2 + Day 3 = 2 * 15.5 = 31 Day 3 + Day 4 = 2 * 16 = 32 Day 4 + Day 5 = 2 * 17 = 34 It is also stated that Day 3 and Day 4 scores are equal: Day 3 = Day 4 = 16
2. Using the equality Day 3 = 16: Day 2 + 16 = 31, which implies Day 2 = 15. Substituting Day 2 = 15 into the first equation: Day 1 + 15 = 30, which implies Day 1 = 15. Therefore, the total score for Day 1 is 15.
3. Day 1 participant ranks are: Akhil: 1 Bimal: 2 Chatur: 3 Chatur's score, being the lowest and a multiple of 3, could be 3, 6, or 9. It is specified that Chatur's minimum score matches Akhil's Day 4 score of 3.
4. Akhil's rank of 1 on Day 1 signifies the highest score for that day.
5. Distributing scores based on the conditions leads to the following table:

   Participants	Score
   Akhil	7
   Bimal	5
   Chatur	3

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

Answer 2

To determine the participant with the highest total score, an analysis of provided data and logical deduction based on given constraints is required.

Data Provided:
- Two-day average scores from Day 2 to Day 5.
- Daily rankings.
- Specific participant score limitations.

Calculation of 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

Derivations from 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

Score Solution:

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

Daily Total Scores:

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

Rank Constraints:

• Chatur's score is consistently a multiple of 3.
• The lowest score on Day 1 matches Akhil's score on Day 4.
• The highest unique score occurred on Day 2.

Chatur's Individual Scores:

• Day 1: 6 (Equivalent to Akhil's Day 4 score)
• Day 2: 9 (Unique and highest score)
• Day 3: 6
• Day 4: 6
• Day 5: 12

Bimal's Individual Scores:

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

Akhil's Individual Scores:

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

Chatur's Cumulative Score: 6 + 9 + 6 + 6 + 12 = 39

Outcome: Chatur achieved the highest total score.

Answer 3

The following table displays the minimum possible total score for 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

According to the table, Bimal's minimum score is 25.

The determined answer is 25.

Answer 4

Below is the final table of Bimal's total scores:

	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

Given that Bimal's total score is a multiple of 3, his score is 27.
This implies Akhil's total score is 23.
Akhil achieved a score of 23 with individual scores of 7, 4, 5, 3, and 4 on Days 1 through 5, respectively.
Therefore, Akhil's score on Day 2 is 4.

Answer 5

Bimal's Total Score

To calculate Bimal's total score, given Akhil's total score is 24, we will proceed systematically.

2-Day Averages:

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

Let the total scores for each day be denoted as follows:

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

Applying the average formulas:

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

The daily total scores are thus:

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

Participants’ Scores

• Chatur: Scores are always multiples of 3.
• Chatur achieved their highest score on Day 2, which was a unique maximum.
• The lowest score on Day 1 is equal to Akhil's score on Day 4, which is \(3\).

Score Distribution:

• Day 1: Chatur = 3, Akhil = 7 (ranked 1st), Bimal = 5
• Day 2: Chatur = 9, Akhil = 4 (ranked 2nd), Bimal = 2 (ranked 3rd)
• Day 3: Chatur = 6, Akhil = 5, Bimal = 5
• Day 4: Chatur = 6, Akhil = 3, Bimal = 7
• Day 5: Chatur = 9, Akhil = 4, Bimal = 5

Summary of Total Scores:

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

Consequently, Bimal's total score is: 26