Solution
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
From the first two statements, we can make the following table :-
In this table first column shows type of campaign amiya chose and first row shows type of campaign ramya chose.
according to clue 1, percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students
where level 1 = staid campaign
and, level 2 = vigorous campaign
therefore in the table - voter turnout will be - 20* (level of campaign of ramya + level of campaign of amiya)
therefore in the table for example if amiya had chose a staid campaign (level 1)
and Ramya also chose a staid campaign (level 1)
then their voter turnout will be = ( 20 \times (1 + 1) = 40% )
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
A and R is the percentage of votes for each candidate which is proportional to the levels of their campaigns.
i.e., if amiya chose vigorous campaign (level 2) while ramya chose staid campaign (level 1)
Then, percentage of votes for each amiya will be 2/3 and for ramya will be 1/3.
Strategy Table
| Amiya ↓ Ramya → | Attack | Issues |
|---|---|---|
| Attack | 10% - A → No Vote 10% - R → No Vote | 10% - A → R 10% - A → No Vote |
| Issues | 20% - R → A 5% - R → No Vote | No change |
This is the table we can form ,from the further information given in the question directly.
Forming a table like this will help us to rationalize and comprehend the data more easily.
Turnout Table
| Amiya ↓ Ramya → | Staid | Vigorous |
|---|---|---|
| Staid | Turnout = 40% A, R = {½, ½} | Turnout = 60% A, R = {⅓, ⅔} |
| Vigorous | Turnout = 60% A, R = {⅔, ⅓} | Turnout = 80% A, R = {½, ½} |
Strategy Table
| Amiya ↓ Ramya → | Attack | Issues |
|---|---|---|
| Attack | 10% - A → No Vote 10% - R → No Vote | 10% - A → R 10% - A → No Vote |
| Issues | 20% - R → A 5% - R → No Vote | No change |
Since we want the maximum possible voting margin, one of them runs a staid campaign and the other person runs a vigorous campaign.
Case 1: Amiya runs a vigorous and Ramya runs a staid campaign.
Total votes turnout = 60%. Amiya receives 40% whereas Ramya receives 20%. Now let us consider Ramya's campaign is attacking, 20% of Ramya's votes go to Amiya and 5% of Ramya's voters did not vote.
Then Amiya receives = 40% + 4% = 44% whereas Ramya receives = 20% - 4% - 1% = 15%.
Margin is 44% - 15% = 29%.
Case 2: Amiya runs a staid and Ramya runs a vigorous campaign.
Total votes turnout = 60%. Amiya receives 20% whereas Ramya receives 40%. Now let us consider Amiya's campaign is attacking, 10% of Amiya's votes go to Ramya and 10% of Amiya's votes did not vote.
Then Ramya receives = 40% + 2% = 42% and Amiya receives = 20% - 2% - 2% = 16%.
Margin is 42% - 16% = 26%.
The maximum possible voting margin is 29%.
Hence, the answer is '29%'