In a market Mrs. Smith and Mrs. Jones sell apples. Mrs. Jones sells her apples for two per shilling. The apples of Mrs. Smith are a bit smaller; she sells hers for three per shilling.

At a certain moment, when both ladies both have the same number of apples left, Mrs. Smith is called away. She asks her neighbour to take care of her goods.

To make everything less complicated, Mrs. Jones simply puts all apples to one big pile, and starts selling them for two shilling per five apples. When Mrs. Smith returns the next day, all apples have been sold. But when they start dividing the money, there appears to be a shortage of seven shilling.

Supposing they divide the number equally, how much does Mrs. Jones lose with this deal?

Each has n apples when the new trading begins.
They make 2n * 2/5 instead of n/2 + n/3 shillings
Thus 5n/6 - 4n/5 = 7
n = 210
They make 168 shillings
Smith makes 84 instead of 70 shillings, gaining 14 shillings
Jones makes 84 instead of 105 shillings, losing 21 shillings

Posted by retiarius on 2004-02-11 09:11:59