Maurice Kraitchik/Mathematical Recreations

Chapter $2$

Problem $41$

Two market-women were selling apples, one at $2$ for $1$ cent and the other at $3$ for $2$ cents.

They had $30$ apples apiece.

In order to end their competition they formed a trust, pooling their stocks and selling the apples at $5$ for $3$ cents.

This was to their advantage because under the new arrangement they took in total $36$ cents.

Under the old system they would have taken a total of only $35$ cents.

Their example was contagious.

Two other women, who also had $30$ apples apiece and who were selling them at $2$ for $1$ cent and $3$ for $1$ cent, formed a trust to sell their apples at $5$ for $2$ cents.

But instead of the $25$ cents which they would have taken in operating separate enterprises, their trust grossed only $24$ cents.

Why?