Question:medium

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 2Day 3Day 4Day 5
1515.51617
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 1Day 2Day 3Day 4Day 5
Akhil12233
Bimal23211
Chatur31122
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)

Updated On: Jan 13, 2026
  • 25
  • 24
  • 28
  • 26
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The Correct Option is D

Solution and Explanation

  • Daily total scores are denoted as $d_1, d_2, d_3, d_4, d_5$.
  • The table provides the following relationships: $d_1 + d_2 = 30$ (Equation 1) $d_2 + d_3 = 31$ (Equation 2) $d_3 + d_4 = 32$ (Equation 3) $d_4 + d_5 = 34$ (Equation 4)

Given information:

  • Day 3 and Day 4 scores are equal: $d_3 = d_4 = 16$.
  • Chatur's Day 2 score is the highest, a multiple of 3.
  • Chatur's lowest score is on Day 1, matching Akhil's Day 4 score.
  • Chatur scored 9 only on Day 2; no other player scored 9 on any given day.
  • Chatur scored 3 only on Day 1. Consequently, Chatur's scores for Days 3, 4, and 5 are 6, 6, and 6, respectively.
  • Akhil's Day 4 score is 3.
  • Bimal's scores on Day 1 and Day 3 are identical. Therefore, Bimal's Day 1 score is 5, implying Akhil's Day 1 score is 7.
  • According to Table 2, Bimal is ranked 3rd on Day 2, and Akhil is ranked 2nd. This indicates Bimal's Day 2 score is lower than Akhil's.

Let Akhil's Day 2 score be $a$ and Bimal's be $b$.

  • The sum of their scores on Day 2 is $15 - (\text{Chatur's Day 2 score})$.
  • Since Chatur's Day 2 score is 9, $a + b = 15 - 9 = 6$.
  • Given Akhil's score is greater than Bimal's ($a>b$), the possible pairs are ($a = 4, b = 2$) or ($a = 5, b = 1$).

The question states Akhil's total score is 24, which leads to Bimal's total score being 26.

Final Answer: 26

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