A king ordered to make a crown from 8 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 underwater gold loses 1/20th of its weight, while silver loses 1/10th. When the crown was weighed underwater, it was 9.25 kg. How much gold was stolen by the goldsmith?
- A1 kg
- B2 kg
- C3 kg
- D4 kg
Explanation
Let g kg be the gold stolen and replaced by silver. Underwater the crown weighs 9.25 kg against 10 kg in air, so it loses 0.75 kg. Gold loses 1/20 of its weight underwater and silver 1/10: (8−g)/20 + (2+g)/10 = 0.75. Multiplying by 20 gives (8−g) + 2(2+g) = 15, i.e. 12 + g = 15, so g = 3. Hence 3 kg of gold was stolen — the classic Archimedes crown problem.