Question

Three participants – Akhil, Bimal and Chatur participate in a random draw competition for five days. Every day, each participant randomly picks up a ball numbered between 1 and 9. The number on the ball determines his score on that day. The total score of a participant is the sum of his scores attained in the five days. The total score of a day is the sum of participants’ scores on that day. The 2-day average on a day, except on Day 1, is the average of the total scores of that day and of the previous day. For example, if the total scores of Day 1 and Day 2 are 25 and 20, then the 2-day average on Day 2 is calculated as 22.5. Table 1 gives the 2-day averages for Days 2 through 5.Table 1: 2-day averages for Days through 5

Day 2| Day 3| Day 4| Day 5
15| 15.5| 16| 17
Participants are ranked each day, with the person having the maximum score being awarded the minimum rank (1) on that day. If there is a tie, all participants with the tied score are awarded the best available rank. For example, if on a day Akhil, Bimal, and Chatur score 8, 7 and 7 respectively, then their ranks will be 1, 2 and 2 respectively on that day. These ranks are given in Table 2. Table 2 : Ranks of participants on each day

| Day 1| Day 2| Day 3| Day 4| Day 5
Akhil| 1| 2| 2| 3| 3
Bimal| 2| 3| 2| 1| 1
Chatur| 3| 1| 1| 2| 2
The following information is also known.
1. Chatur always scores in multiples of 3. His score on Day 2 is the unique highest score in the competition. His minimum score is observed only on Day 1, and it matches Akhil’s score on Day 4.
2. The total score on Day 3 is the same as the total score on Day 4.
3. Bimal’s scores are the same on Day 1 and Day 3.
If Akhil attains a total score of 24, then what is the total score of Bimal? (This Question was asked as TITA)

• A. 25
• B. 24
• C. 28
• D. 26

Answer 1

Answer: (D)

26

Answer 2

• We have the total scores for each day: 𝑑1,𝑑2,𝑑3,𝑑4,​, and d 5​.
  • The table gives us: 𝑑1+𝑑2=30 (equation 1), 𝑑
    2+𝑑3=31 (equation 2),
    𝑑3+𝑑4=32 (equation 3), and
    𝑑4+𝑑5=34 (equation 4).

Given:

• Total scores on Day 3 and Day 4 are the same, so 𝑑3=𝑑4=16 d
• Chatur's score on Day 2 is the highest in the competition and is a multiple of 3.
• Chatur's minimum score is on Day 1, which matches Akhil's score on Day 4.
• Chatur scored 9 only once, on Day 2, and no one else scored 9 on any of the given days.
• Chatur scored 3 only once, on Day 1. Therefore, Chatur's scores on Day 3, Day 4, and Day 5 are 6, 6, and 6 respectively.
• Akhil's score on Day 4 is 3.
• Bimal's scores on Day 1 and Day 3 are the same. So, Bimal's score on Day 1 is 5, which means Akhil's score on Day 1 is 7.
• From Table 2, Bimal is ranked 3rd on Day 2, and Akhil is ranked 2nd on Day 2. So, Bimal's score on Day 2 is less than Akhil's.

Let's denote Akhil's score on Day 2 as 𝑎 a and Bimal's score as b.

• Then, 9+𝑎+𝑏=15, and since Akhil's score is greater than Bimal's on Day 2, 𝑎+𝑏=6
• This implies Akhil's score could be $\frac{4}{5}$ and Bimal's could be $\frac{2}{1}$.

In the question, it is given that the score obtained by Akhil is 24, which implies the score obtained by Bimal is 26. The answer is 26.