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.
What is the minimum possible total score of Bimal? (This Question was asked as TITA)
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.
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.
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.
What is the minimum possible total score of Bimal? (This Question was asked as TITA)
| Table 1: 2-day averages for Days through 5 | |||
|---|---|---|---|
| Day 2 | Day 3 | Day 4 | Day 5 |
| 15 | 15.5 | 16 | 17 |
| 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 |
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.
What is the minimum possible total score of Bimal? (This Question was asked as TITA)
Updated On: Sep 17, 2024
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The Correct Option is B
Solution and Explanation
The value of a can be \(\frac{4}{5}\), and the value of b can be \(\frac{2}{1}\).
Let's consider this following table:
| Day 1 | Day 2 | Day 3 | Day 4 | Day 5 | Total Score | |
| Akhil | 7 | \(\frac{4}{b}\) | b | 3 | \(\frac{3}{4}\) | 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 possible total score of Bimal will be 25.
So, the correct option is (B): 25.
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3. Bimal’s scores are the same on Day 1 and Day 3.
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