Question

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. Did Alan break even? If not, did he have a profit or loss and by how much?

Answer 1

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:

$loss\ \% = (\frac{x}{10})^2$

Here, x = 25

$loss\ \% = (\frac{25}{10})^2\\\\loss\ \% = 2.5^2\\\\loss\ \% = 6.25$

Thus the loss percentage is 6.25 %