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An Apple A Day (Posted on 2004-02-11) Difficulty: 2 of 5
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?

  Submitted by Ravi Raja    
Rating: 3.1429 (7 votes)
Solution: (Hide)
The big pile of apples contains the same amount of large apples of half a shilling each (from mrs. Jones), as smaller apples of one third shilling each (from mrs. Smith). The average price is therefore (1/2 + 1/3)/2 = 5/12 shilling. But the apples were sold for 2/5 shilling each (5 apples for 2 shilling). Or: 25/60 and 24/60 shilling respectively. This means that per sold apple there is a shortage of 1/60 shilling. The total shortage is 7 shilling, so the ladies together started out with 420 apples. These are worth 2/5 × 420 = 168 shilling, or with equal division, 84 shilling for each. If Mrs. Jones would have sold her apples herself, she would have received 105 shilling.
Mrs. Jones loses 21 shilling in this deal.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2021-12-25 05:58:30
answerK Sengupta2007-12-07 06:14:45
QuestionNo SubjectJohnny2004-10-09 19:00:26
SolutionSolution (no applet used)Penny2004-02-11 09:17:32
aplles and orangesretiarius2004-02-11 09:11:59
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