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?

OK, I'll bite. This may not be the core solution.

After reading retiarius's solution, I realize that I interpreted "there appears to be a shortage of seven shillings" differently than he did. My original answer appears as a footnote.

Lets say each woman put N apples in the pile.

(4/5)N = (1/2)N + (1/3)N - 7

N = 210

Mrs Jones should have gotten 105 shillings, but actually got 84 shillings. She lost 21 shillings.

Footnote: My original solution read:

Mrs. Jones meant to sell these apples for
(2/5)*(2N) = (4/5)N shillings, but the amount was found to be (4/5)N - 7 shillings.

Each woman got [(4/5)N - 7]/2 =(2/5)N - 7/2 shillings

Mrs. Jones whould have gotten N/2 shillings if she hadn't given them to Mrs. Smith.

Mrs. Jones lost N/2 - [(2/5)N - 7/2]
= (1/10)N + 7/2 shillings


Edited on February 11, 2004, 9:31 am

Posted by Penny on 2004-02-11 09:17:32