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Convent Garden Problem



Here is a puzzle known as the Covent Garden Problem, which appeared in London half a century ago, accompanied by the somewhat surprising assertion that it had mystified the best mathematicians of England:

Mrs. Smith and Mrs. Jones had equal number of apples but Mrs. Jones had larger fruits and was selling hers at the rate of two for a penny, while Mrs. Smith sold three of hers for a penny.

Mrs. Smith was for some reason called away and asked Mrs. Jones to dispose of her stock. Upon accepting the responsibility of disposing her friend's stock, Mrs. Jones mixed them together and sold them of at the rate of five apples for two pence.

When Mrs. Smith returned the next day the apples had all been disposed of, but when they came to divide the proceeds they found that they were just seven pence short, and it is this shortage in the apple or financial market which has disturbed the mathematical equilibrium for such a long period.

Supposing that they divided the money equally, each taking one-half, the problem is to tell just how much money Mrs. Jones lost by the unfortunate partnership?

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Say they had x no. of apples each.

Cost of Mrs. Smith’s apples = x/3 penny
Cost of Mrs. Jones’ apples = x/2 penny
Real cost of total apples = x/3 + x/2 = 5x/6 penny
Cost of 2x no. of apples sold by Mrs. Jones = 4x/5 penny
The difference was 7 penny short.
So 5x/6 – 4x/5 = 7
Solving this we get x = 210 No.
Mrs. Smith should have got = 210/3 = 70 penny.
Mrs. Jones should have got = 210/2 = 105 penny
Mrs. Smith sold total 420 No. apples for = 4*210/5 = 168 penny
They divided it equally each taking one-half, so each got = 168/2 = 84 penny.
Mrs. Jones lost 105 – 84 = 21 penny.

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