At the end of the year, Town X had 12,741 people and Town Y had 24,366 people. If 1,024 people moved from Town Y to Town X, we can calculate the new populations as follows:
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New Population of Town X: \[ \text{New Population of Town X} = 12,741 + 1,024 = 13,765 \]
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New Population of Town Y: \[ \text{New Population of Town Y} = 24,366 - 1,024 = 23,342 \]
So, the populations now are:
- Town X: 13,765 people
- Town Y: 23,342 people