Question 165
Archimedes has a two-plate scale with arms of different lengths. Aiming to weigh two kilos of sugar, he proceeded as follows: he put a weight of one kilo on the left plate and sugar on the other side until the scale was balanced. Then he emptied the two plates, put the weight of one kilo on the right plate and sugar on the left plate until the two dishes were balanced. Adding the two amounts of sugar in these weighings, did he get less than two kilos, more than two kilos or exactly two kilos? Note: For balance to occur, the weights on the plates must be inversely proportional to the lengths of the corresponding arms. 