Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya’s and Ramya’s campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. If Amiya and Ramya both run campaigns focusing on issues, then
- The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then 20 × (2 + 2)%, that is, 80% of the students will vote in the election.
- Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive 1/3 of the votes cast, and Ramya will receive the other 2/3.
The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent. - If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then 10% of the students who would have otherwise voted for Amiya will vote for Ramya, and another 10% who would have otherwise voted for Amiya, will not vote at all.
- If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then 20% of the students who would have otherwise voted for Ramya will vote for Amiya, and another 5% who would have otherwise voted for Ramya, will not vote at all.
- If both run campaigns attacking each other, then 10% of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.
Q. 1 If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?
1) 64% 2) 36% 3) 60% 4) 40%
Q. 2 What is the minimum percentage of students who will vote in the election?
1) 36% 2) 40% 3) 32% 4) 38%
Q. 3 If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she can get?
1) 44% 2) 40% 3) 48% 4) 36%
Q. 4 If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?
1) 12% 2) 18% 3) 15% 4) 30%
Q. 5 What is the maximum possible voting margin with which one of the candidates can win?
1) 28% 2) 26% 3) 29% 4) 20%
✅ Solution
- Campaign Level:
- Staid = 1
- Vigorous = 2
- Turnout (%) = 20 × (Sum of levels)
- Vote Share (%) = Proportional to campaign levels unless altered by attack campaigns
| Amiya Campaign | Ramya Campaign | Turnout (%) | Initial Votes (A:R) | Final Votes (A:R) After Attack |
| Vigorous, Issues | Staid, Attack | 60% | 40% : 20% | A = 44%, R = 15% (max margin case) |
| Staid, Issues | Vigorous, Attack | 60% | 20% : 40% | A = 28%, R = 30% |
| Staid, Attack | Staid, Attack | 40% × 90% = 36% | 20% : 20% | A = 18%, R = 18% |
🔸 Q6. If both run staid campaigns attacking the other, what % of students vote?
- Level = 1 (Amiya) + 1 (Ramya) = 2
- Turnout without attack = 20 × 2 = 40%
Now since both attack, 10% of each candidate’s original voters do not vote (as per rule 3 in Step 2 of the image)
- Final turnout = 90% of 40% = 36%
✅ Answer: 2) 36%
🔸 Q7. Minimum % of students who will vote?
Try lowest turnout cases with maximum penalty.
Case: Both staid campaigns, both attacking
- Turnout = 20 × (1+1) = 40%
- Due to mutual attack: only 90% of voters vote → 40% × 0.9 = 36%
Try any lower?
- 1 (staid) + 1 (staid) is minimum sum.
- Attack always reduces votes, but not below 36% (already lowest combo).
✅ Answer: 1) 36%
🔸 Q8. If Amiya focuses on issues, what is max % of votes she can get?
We want max votes for Amiya:
- So she focuses on issues.
- Ramya should attack her → because this benefits Amiya (Rule 2 in Step 2).
Let’s use:
- Amiya = vigorous (level 2), Ramya = staid (level 1)
- Total turnout = 20 × (2 + 1) = 60%
- Vote ratio without adjustments: Amiya 2/3 of 60% = 40%, Ramya = 20%
Ramya attacks →
- 20% of Ramya’s 20% = 4% goes to Amiya
- 5% of Ramya’s 20% = 1% doesn’t vote
So, final:
- Amiya = 40% + 4% = 44%
- Ramya = 20% − 4% − 1% = 15%
- Turnout = 60% − 1% = 59%
(but % is out of 100%, so we consider Amiya’s 44%)
✅ Answer: 1) 44%
🔸 Q9. If Ramya attacks Amiya, what is the minimum % she is guaranteed to get?
We want worst-case for Ramya when she attacks:
- So Amiya should be vigorous on issues (strongest case)
- Ramya = staid attacking
Turnout = 20 × (2 + 1) = 60%
Normal share: Amiya = 2/3 of 60% = 40%, Ramya = 20%
Now since Ramya attacks:
- 20% of her 20% = 4% goes to Amiya
- 5% of 20% = 1% doesn’t vote
So Ramya’s final votes: 20% − 4% − 1% = 15%
✅ Answer: 3) 15%
🔸 Q10. Max possible voting margin?
Try both extreme cases.
Case 1:
- Amiya vigorous issues (2), Ramya staid attack (1)
- Turnout = 60%, initial votes: Amiya = 40%, Ramya = 20%
Ramya attacks:
- Amiya: 40% + 4% = 44%
- Ramya: 20% − 4% − 1% = 15%
Margin = 44 − 15 = 29%
Case 2:
- Amiya staid issues (1), Ramya vigorous attack (2)
- Turnout = 60%, initial: Amiya = 20%, Ramya = 40%
Ramya attacks:
- Amiya: 20% + 8% = 28%
- Ramya: 40% − 8% − 2% = 30%
Margin = 30 − 28 = 2% → Lower than 29%
✅ Final Answer: 3) 29%
