A group of people was surveyed about whether the council should collect recycling once a week instead of once a fortnight. Two-thirds of the people said ‘Yes’, and one-third said ‘No’.

Question

A year later the same group of people was surveyed again and this time one-quarter of them had changed their minds, resulting in a tie between the ‘Yes’ and ‘No’ votes.
Of the people who originally voted ‘Yes’, what fraction changed their minds?

Answer 1

Let x be the number who changed from No to Yes
Let y be the number who changed from Yes to No
If there were n people altogether, then
1/3 n - x + y = 2/3 n - y + x
x + y = 1/4 n
or,
y-x = 1/6 n
y+x = 1/4 n
So, y = 5/24 n
But we want the fraction of the original Yes voters, so
(5/24 n) / (2/3 n) = 5/16