No Alan did not break even
Alan incured a loss of 6.25 %
Solution:
Given that,
Alan bought two bikes
He sold one to Beth for $300 taking a 25% loss
He also sold one to Greta for $300 making a 25% profit
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss
Which is given as:
[tex]loss\ \% = (\frac{x}{10})^2[/tex]
Here, x = 25
[tex]loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25[/tex]
Thus the loss percentage is 6.25 %
