In an election several candidates contested for a constituency. In any constituency, the winning candidate was the one who polled the highest number of votes, the first runner up was the one who polled the second highest number of votes, the second runner up was the one who polled the third highest number of votes, and so on. There were no ties (in terms of number of votes polled by the candidates) in any of the constituencies in this election.
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.
The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election. Constituency
A B C D No. of candidates contesting 10 12 5 8 Total No. of valid votes polled 5,00,000 3,25,000 6,00,030 No. of votes polled by the winning candidate 2,75,000 48,750 No. of votes polled by the first runner up 95,000 37,500 No. of votes polled by the second runner up 30,000 % of valid votes polled by the third runner up 10%
The following additional facts are known:
1. The first runner up polled 10,000 more votes than the second runner up in constituency A.
2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
How many candidates who contested in constituency B lost their security deposit? [This Question was asked as TITA]
In an electoral system, a security deposit is the sum of money that a candidate is required to pay to the election commission before he or she is permitted to contest. Only the defeated candidates (i.e., one who is not the winning candidate) who fail to secure more than one sixth of the valid votes polled in the constituency, lose their security deposits.
The following table provides some incomplete information about votes polled in four constituencies: A, B, C and D, in this election.
Constituency | ||||
|---|---|---|---|---|
| A | B | C | D | |
| No. of candidates contesting | 10 | 12 | 5 | 8 |
| Total No. of valid votes polled | 5,00,000 | 3,25,000 | 6,00,030 | |
| No. of votes polled by the winning candidate | 2,75,000 | 48,750 | ||
| No. of votes polled by the first runner up | 95,000 | 37,500 | ||
| No. of votes polled by the second runner up | 30,000 | |||
| % of valid votes polled by the third runner up | 10% | |||
The following additional facts are known:
1. The first runner up polled 10,000 more votes than the second runner up in constituency A.
2. None of the candidates who contested in constituency C lost their security deposit. The difference in votes polled by any pair of candidates in this constituency was at least 10,000.
3. The winning candidate in constituency D polled 5% of valid votes more than that of the first runner up. All the candidates who lost their security deposits while contesting for this constituency, put together, polled 35% of the valid votes.
How many candidates who contested in constituency B lost their security deposit? [This Question was asked as TITA]
- 9
- 13
- 8
- 11
The Correct Option is D
Solution and Explanation
Constituency A Analysis
Total Votes Cast:
- Constituency A recorded a total of 500,000 valid votes.
Security Deposit Threshold:
- To retain their security deposit, a candidate needed to secure at least 1/6th of the total valid votes, calculated as \( \frac{1}{6} \times 500,000 = 83,334 \) votes.
Vote Distribution Among Top Candidates:
- Winner: 275,000 votes.
- 1st Runner-up: 95,000 votes (10,000 more than the 2nd runner-up).
- 2nd Runner-up: 85,000 votes.
- Combined votes for these three: 275,000 + 95,000 + 85,000 = 455,000 votes.
Votes for Other Candidates:
- The remaining candidates collectively received 500,000 - 455,000 = 45,000 votes.
Candidates Forfeiting Security Deposit:
- As the collective vote count for the remaining candidates (45,000) is less than the individual threshold (83,334), all these candidates forfeited their security deposits.
Vote Percentage Analysis:
- The proportion of votes obtained by candidates who lost their security deposit is \( \frac{45,000}{500,000} \times 100 = 9\% \).
Therefore, for constituency A:
- The percentage of votes secured by candidates who forfeited their security deposit is 9%.
Constituency C Analysis
Key Information:
- No candidate in constituency C lost their security deposit.
- The minimum vote difference between any two candidates was 10,000.
Vote Distribution Pattern:
- The 5th highest vote-getter must have polled more than \( \frac{600,030}{6} = 100,006 \) votes.
- Given the minimum 10,000 vote difference, the vote distribution is as follows:
- Winner: 140,006 votes.
- 1st Runner-up: 130,006 votes.
- 2nd Runner-up: 120,006 votes.
- 3rd Runner-up: 110,006 votes.
- 4th Runner-up: 100,006 votes.
- The sum of votes for these top five candidates is 600,030.
Constituency D Information
- Provided Data:
- The total votes in constituency D are represented as 100x.
- The winning candidate's vote count is given by \( 15x + 37,500 \).
Updated Summary Table
The following table summarizes the data:
| Constituency | Total Votes | Winner Votes | 1st Runner-Up Votes | 2nd Runner-Up Votes | 3rd Runner-Up Votes | 4th Runner-Up Votes | 5th Highest Votes | Total of Top 5 Votes |
|---|---|---|---|---|---|---|---|---|
| A | 500,000 | 275,000 | 95,000 | 85,000 | - | - | - | 455,000 |
| C | 600,030 | 140,006 | 130,006 | 120,006 | 110,006 | 100,006 | >100,006 | 600,030 |
| D | 100x | 15x+37,500 | - | - | - | - | - | - |
Summary of Findings:
- Constituency A: 9% of the votes were cast for candidates who forfeited their security deposit.
- Constituency C: The table indicates the vote distribution, ensuring all candidates retained their security deposits.
- Constituency D: Insufficient information is available to provide a complete analysis.
In constituency B, the minimum votes required to secure the deposit was \( \frac{1}{6} \times 325,000 = 54,167 \). Since the winner received fewer than 54,167 votes, all other candidates also failed to meet this threshold and lost their security deposits. Consequently, 11 candidates lost their security deposits in constituency B.
Top Questions on Tables
Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators- Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes to) and received from (incoming minutes from) these friends, grouped by the operators. Some of the entries are missing.
Operator Xitel Operator Yocel
It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from:
• Bijay to Eshan,
• Chetan to Anu and Chetan to Deepak,
• Deepak to Bijay and Deepak to Faruq,
• Eshan to Chetan and Eshan to Deepak.- Odsville has five firms – Alfloo, Bzygoo, Czechy, Drjbna and Elavalaki. Each of these firms was founded in some year and also closed down a few years later.
Each firm raised Rs. 1 crore in its first and last year of existence. The amount each firm raised every year increased until it reached a maximum, and then decreased until the firm closed down. No firm raised the same amount of money in two consecutive years. Each annual increase and decrease was either by Rs. 1 crore or by Rs. 2 crores.
The table below provides partial information about the five firms.What is the largest possible total amount of money (in Rs. crores) that could have been raised in 2013? (This Question was asked as TITA)Firm First year of existence Last year of existence Total amount raised (Rs. crores) Alfloo 2009 2016 21 Bzygoo 2012 2015 Czechy 2013 9 Drjbna 2011 2015 10 Elavalaki 2010 13 - 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.
Table 1: 2-day averages for Days through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 The following information is also known.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) - 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.
Table 1: 2-day averages for Days through 5 Day 2 Day 3 Day 4 Day 5 15 15.5 16 17 The following information is also known.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.
If Akhil attains a total score of 24, then what is the total score of Bimal? (This Question was asked as TITA) - Want to practice more? Try solving extra ecology questions todayView All Questions