# Problem 236: Luxury Hampers

![graphic](img236.gif)

Suppliers 'A' and 'B' provided the following numbers of products for the
luxury hamper market: Product'A''B'Beluga Caviar5248640Christmas
Cake13121888Gammon Joint26243776Vintage Port57603776Champagne
Truffles39365664 Although the suppliers try very hard to ship their
goods in perfect condition, there is inevitably some spoilage - i.e.
products gone bad. The suppliers compare their performance using two
types of statistic:The five per-product spoilage rates for each supplier
are equal to the number of products gone bad divided by the number of
products supplied, for each of the five products in turn. The overall
spoilage rate for each supplier is equal to the total number of products
gone bad divided by the total number of products provided by that
supplier.To their surprise, the suppliers found that each of the five
per-product spoilage rates was worse (higher) for 'B' than for 'A' by
the same factor (ratio of spoilage rates), m>1; and yet,
paradoxically, the overall spoilage rate was worse for 'A' than for 'B',
also by a factor of m. There are thirty-five m>1 for which this
surprising result could have occurred, the smallest of which is
1476/1475. What's the largest possible value of m? Give your answer as a
fraction reduced to its lowest terms, in the form u/v.