Henry Ernest Dudeney/Modern Puzzles/187 - Weighing the Goods/Solution

by : $187$

 * Weighing the Goods
 * A tradesman whose morals had become corrupted during the war by a course of profiteering went to the length of introducing a pair of false scales.
 * It will be seen from the diagram that one arm is longer than the other,
 * though they are purposely drawn so as to give no clue as to the answer.


 * Dudeney-Modern-Puzzles-187.png


 * As a consequence, it happened that in one of the cases exhibited eight of the little packets
 * (it does not matter what they contain)
 * exactly balanced three of the canisters,
 * while in the other case one packet appeared to be of the same weight as $6$ canisters.
 * Now, as the true weight of one canister was known to be exactly one ounce, what was the true weight of the eight packets?

Solution

 * $8$ packets weigh $12$ ounces.

Proof
Let the arms of the balance be $x$ and $y$.

Let $P$ and $C$ ounces be the weights of package and canister respectively.

From the laws of physics and the rubric of the question:

We are given that $C = 1$.

So $P = \dfrac 3 2$ and so $8 P = 12$.