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Some 40 percent of people's "first memory" happened at an age when it wasn't possible to create memories.

Source

Context shows the percentage is about the people. The word memory, being singular, also indicates the percentage is about the people. Without context, would you be able to infer which is meant if we changed the sentence to:

Some 40 percent of people's first memories ...

And what about this one:

20 percent of the countries' money came from tourism.

Is there any rule for the structure "n % of X's Y"?

  • X only modifies Y. It has no bearing on the calculation. So "40 percent of memories" and "20 percent of the money" basically mean the same thing. – user3169 Sep 2 '18 at 5:42
  • Does that mean the writer of the cited headline made a mistake? – Sara Sep 2 '18 at 6:39
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    No, it is still "40 percent of memories", where "memories" are being counted. *people's" just tells us whose memories are being counted, but the example does not count people. – user3169 Sep 2 '18 at 18:30
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    You should include such text in your question. Links are OK for reference, but pertinent information should be in the question. – user3169 Sep 2 '18 at 20:40
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    Maybe it was written poorly, though in reality the applicable person to false first memory ratio is 1:1. Or person to first memory in fact. – user3169 Sep 2 '18 at 20:45
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In your example, the object of the preposition is

memories

So many would understand it to mean "less than half of one's first memories".

If it is meant as you say, it might be

For 40% of the people, their first memories...

The percentage is associated with the object of the preposition of.
A percentage of something.

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