THE HONEST DAIRYMAN.
(
Measuring, Weight, and Packing Puzzles.)
An honest dairyman in preparing his milk for public consumption employed
a can marked B, containing milk, and a can marked A, containing water.
From can A he poured enough to double the contents of can B. Then he
poured from can B into can A enough to double its contents. Then he
finally poured from can A into can B until their contents were exactly
equal. After these operations he would send the can A to London, and the
puzzle is to discover what are the relative proportions of milk and
water that he provides for the Londoners' breakfast-tables. Do they get
equal proportions of milk and water--or two parts of milk and one of
water--or what? It is an interesting question, though, curiously enough,
we are not told how much milk or water he puts into the cans at the
start of his operations.
Answer:
Whatever the respective quantities of milk and water, the relative
proportion sent to London would always be three parts of water to one of
milk. But there are one or two points to be observed. There must
originally be more water than milk, or there will be no water in A to
double in the second transaction. And the water must not be more than
three times the quantity of milk, or there will not be enough liquid in
B to effect the second transaction. The third transaction has no effect
on A, as the relative proportions in it must be the same as after the
second transaction. It was introduced to prevent a quibble if the
quantity of milk and water were originally the same; for though double
"nothing" would be "nothing," yet the third transaction in such a case
could not take place.
