Mindyard | Directions (Q.42-Q.46): 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, the 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. If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election? 60%, 36%, 64%, 40%

Directions (Q.42-Q.46): 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, the

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.

If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?

Options

60%

36%

64%

40%

Correct Answer :

Option B

36%

Solution :

The correct option is 36%.

To find the percentage of students voting in the election when both candidates run staid campaigns attacking each other, we can break down the calculations step-by-step:

Step 1: Determine the campaign levels
A campaign is described as "staid" if it has a level of 1, and "vigorous" if it has a level of 2.
Since both Amiya and Ramya run staid campaigns:
Amiya's campaign level (L_A) = 1
Ramya's campaign level (L_R) = 1

Step 2: Calculate the voting percentages if they focused on issues
According to the rules, if both candidates focus on issues, the percentage of students voting in the election is 20 times the sum of their campaign levels:
Percentage of voters = 20 × (L_A + L_R)%
Substituting the levels:

$20 \times (1 + 1) % = 20 \times 2 % = 40 %$
So, 40% of the total student population would vote if they focused on issues.

Among these voting students, the votes received by each candidate are proportional to their campaign levels. Since both have a campaign level of 1, the votes are shared equally (1 : 1):
Amiya's share of votes = 1/2 of the voting students = 20% of the total student population.
Ramya's share of votes = 1/2 of the voting students = 20% of the total student population.

Step 3: Adjust for attacking campaigns
The rules state that if both candidates run campaigns attacking each other, then 10% of the students who would have otherwise voted for each candidate (had they run campaigns focusing on issues) will not vote at all.

We calculate the updated voting percentages for each candidate's prospective voters:
Amiya's adjusted voter percentage:

$20 % \times (1 - 0.10) = 20 % \times 0.90 = 18 %$
Ramya's adjusted voter percentage:

$20 % \times (1 - 0.10) = 20 % \times 0.90 = 18 %$

Step 4: Calculate the total voting percentage
The total percentage of students who will vote in the election is the sum of the adjusted voter percentages for both candidates:
Total voting percentage = 18% + 18% = 36%.

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