A king ordered to make a crown from S kg of gold and 2 kg of silver. The goldsmith took away some amount of gold and replaced it by an equal amount of silver and the crown when made, weighed 10 kg. The king knows that under water gold loses —th of & u its weight, while silver loses When the crown was weighed under water, it wa$ 9-25 kg. How much gold was stolen by the goldsmith?

The problem involves Archimedes' principle and buoyancy. Initially, the king provided 8 kg of gold and 2 kg of silver for a 10 kg crown. Let x be the amount of gold stolen and replaced by silver. The final crown contains (8 - x) kg of gold and (2 + x) kg of silver. Under water, gold loses 1/20th of its weight (retaining 19/20) and silver loses 1/10th (retaining 9/10). The total apparent weight in water is given as 9.25 kg. Setting up the equation: (8 - x) * (19/20) + (2 + x) * (9/10) = 9.25. Simplifying this: 0.95(8 - x) + 0.9(2 + x) = 9.25, which leads to 7.6 - 0.95x + 1.8 + 0.9x = 9.25. This simplifies to 9.4 - 0.05x = 9.25, resulting in 0.05x = 0.15, so x = 3 kg. Thus, 3 kg of gold was stolen.