I OM - B - Task 3


Someone has an unbalanced two-pan scale (i.e., a scale
whose arms are unequal). Wanting to weigh 2 kg of sugar, they proceed
as follows: they place a 1 kg weight on the left pan of the scale,
and pour sugar onto the right pan until it balances; then:
after emptying both pans, they place the 1 kg weight on the right pan, and pour sugar onto the left pan until it balances. Do the two
amounts of sugar weighed in this way together weigh less, or more, or exactly
2 kg?
Let's denote the amount of sugar weighed for the first time by $ x $, and for the second time by $ y $. The lengths of the arms of the balance are $ p $ and $ q $, where $ p \neq q $.

According to the lever law (Fig. l) we have:






Therefore,






since






Answer: More than 2 kg of sugar was weighed in total.