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Paradox or Not?

A Paradox submitted by F.R.S.

Take a third of a number,
And it will to your wonder,
In value one half increas’d be;
And if two thirds you take,
The remainder will make,
The whole and two thirds, you will see.
Now ye high learned sages,
Whose wit will to ages,
With splendour and glory abound;
Explain this strange truth,
To our unlearned youth,
And they will your trump of fame sound.

Solution:

Source: The Gentleman’s Mathematical Companion, 1801