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Weigh Way

A merchant had a fradulant balance: He buys in on the shorter arm, and sells out on the longer, and thereby gains 5.19395 percent. But if the longer arm measured half an inch more, the shorter remains unaltered, his gain would be 11.8713 percent. Required the length of each arm of the beam.

Solution: 16 inch and 15.6 inch.

The solution from the text is given, only because I am still trying to figure out the question!

Source: John Hunter's Text-book of Arithmetic, for the Use of Teachers, 1847