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

The Correct Option is D

• We have the total scores for each day: $d_1, d_2, d_3, d_4,$ and $d_5$.
• The table gives us: 
  $d_1 + d_2 = 30$   (Equation 1), 
  $d_2 + d_3 = 31$   (Equation 2), 
  $d_3 + d_4 = 32$   (Equation 3), 
  $d_4 + d_5 = 34$   (Equation 4) 

Given:

• Total scores on Day 3 and Day 4 are the same, so $d_3 = d_4 = 16$.
• 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 Akhil's score on Day 2 be $a$ and Bimal's be $b$.

• Then, $9 + a + b = 15$
• So, $a + b = 6$, and since Akhil's score is greater than Bimal's, possible values are $a = 4$, $b = 2$ or $a = 5$, $b = 1$.

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

Final Answer: 26