Propositiones ad Acuendos Juvenes/Problems/6 - De Duobis Negotiatoribus C Solidos Communis Habentibus

by : Problem $6$

 * De Duobis Negotiatoribus C Solidos Communis Habentibus: $2$ Wholesalers with $100$ Shillings
 * $2$ wholesalers with $100$ shillings between them bought some pigs with the money.
 * They bought at the rate of $5$ pigs for $2$ shillings, intending to fatten them up and sell them again, making a profit.
 * But when they found that it is not the right time of year for fattening pigs,
 * and they were not able to feed them through the winter,
 * they tried to sell them again to make a profit.
 * But they couldn't, because they could only sell them for the price they had paid for them, $2$ shillings for $5$ pigs.
 * When they saw this, they said to each other, "Let's divide them.
 * By dividing them, and selling them again at the rate they had bought them for, they made a profit.
 * How could they be divided to make a profit, which could not be made by selling them all at once?

Solution
First there were $250$ pigs bought with $100$ shillings at the above mentioned rate, for $5$ fifties are $250$.

On division, each merchant had $125$ pigs.

One sold the poorer quality pigs at $3$ for a shilling.

The other sold the better quality pigs at $2$ for a shilling.

The one who sold the poorer quality pigs received $40$ shillings for $120$ pigs.

The one who sold the better quality pigs received $60$ shillings for $120$ pigs.

Then there remained $5$ of each sort of pig.

From these they could make a profit of $4$ shillings and $2$ pence.