One of the benefits of using Trade Extensions for online sourcing is that during the analysis phase you can be sure you comparing like with like – or apples with apples as the saying goes. Here, in a puzzle popularly known as the Covent Garden Problem, you can test your true apple comparing skills.
Mrs. Smith and Mrs. Jones both had an equal number of apples. But because Mrs. Jones had larger fruits, she was selling her apples at two for a penny. Mrs. Smith who had more modest fruits sold hers at three for a penny.
During a thick London fog, Mrs. Smith was called away and she asked Mrs. Jones to sell her apples in her absence. Mrs Jones happily accepted the responsibility of selling her friend's stock and, to save time, she mixed the apples together and set the price at five apples for two pence. All the apples were sold.
The ladies knew how much money they usually made but when they counted the proceeds they found the total was seven pence short of what they expected.
Mrs Jones felt particularly short-changed and the challenge is as follows:
Calculate just how much money Mrs Jones lost by the unfortunate partnership if the money was divided equally i.e. each taking one-half.
The Solution
Mrs Jones lost 21 pence
The mixed apples were sold at five apples for two pence. Therefore the total number of apples must have been a multiple of five e.g. 5, 10, 15, 20, 25, 30,…, 60, 65,…etc.
Because Mrs Jones sold apples in groups of two and Mrs Smith sold apples in groups of three, the minimum number of apples they could have together is 60.
If the apples were sold separately, 30 of Mrs. Smith’s apples would fetch 10 pence and 30 of Mrs. Jones's would fetch 15 pence. Therefore when sold separately, 60 apples would fetch 25 pence altogether (i.e. 10+15).
However, when sold together at 5 apples for 2 pence, 60 apples would fetch 24 pence
i.e. (60÷5) x 2. This represents a loss of 1 pence compared to the money generated selling the apples separately.
As the ladies lost 7 pence altogether, they must have had 420 apples between them to start with (i.e. 60 x 7). This would have earned them 168 pence i.e. (420÷5) x 7 which means both ladies earned 84 pence.
However, because Mrs. Jones could have sold her 210 apples for 105 pence (210÷2) she actually lost 21 pence (105 – 84).
The flip side is that while Mrs. Jones lost 21 pence despite doing all the work, Mrs. Smith earned 84 pence when she would have only made 70 pence if she sold her apples herself.
The moral of the story is that even when you are comparing apples with apples, make sure they are the same size apples – especially when it’s foggy.