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 |
The minimum percentage of students voting in the election when both of the campaigns are staid and attacking.
since, if one candidate runs an attacking campaign whereas the other candidate runs an issues campaign, a fair number of voters get transferred to the other candidate's vote share.
And if both the campaigns are staid and attacking - which we already found previous question.
Total votes turnout = 20 * (1 + 1)% = 40%.
Amiya receives ½(40%) = 20% whereas Ramya also receives ½(40%) = 20%.
Since both are attacking, 10% of the Amiya and Ramya votes don’t turn up. Therefore, each will receive only 20% - (10% of 20%) = 18%.
Percentage of students who will vote in the election = 18% + 18% = 36%.
Hence, the answer is '36%'