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Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam
Amiya runs a campaign on issues, and we need to find the maximum vote share that she can get.
We are trying to maximise the number of voters for Amiya, that means Amiya needs to run a vigorous campaign.
Since, we are trying to increase the vote share for Amiya, we want as many voters as possible transferred from Ramya's share to Amiya's votes.
As the number of votes a candidate receives is proportional to the intensity level of the campaign, we want Ramya also to run a vigorous AND attacking campaign, so that her votes are transferred to Amiya.
In this scenario we have 20 × (2 + 2)% of the people voting, 80% of the people. Of that, if both had ran issues campaign, they would have each received 40% of the votes.
Now, we want Ramya to run an attacking campaign, where 20% of the people that would have voted for her vote for Amiya.
So 20% of 40% of the votes are transferred to Amiya. That is 8% of the votes. And we are also told that, 5% that would have voted for her dont vote, so 5% of 40% dont vote, that is 2% of the voters.
Final Tally is Amiya gets 48% of the votes, and Ramya gets 30% of the votes.