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, weighted 10 kg. The king knows that under water gold loses \(\frac{1}{20}th\) of its weight, while silver loses \(\frac{1}{10}th\). When the crown was weighted under water, it was 9.25 kg. How much gold was stolen by the goldsmith?
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, weighted 10 kg. The king knows that under water gold loses \(\frac{1}{20}th\) of its weight, while silver loses \(\frac{1}{10}th\). When the crown was weighted under water, it was 9.25 kg. How much gold was stolen by the goldsmith? Correct Answer 3 kg
Given:
Weight of gold = 8 kg
Weight of silver = 2 kg
Total weight (under water) = 9.25 kg
Calculation:
Let goldsmith took x amount of gold and added x amount of silver
Now the weight of gold = 8 - x
The weight of silver = 2 + x
Weight loses in underwater = 10 - 9.25 = 0.75 kg
According to condition,
+ = 0.75
⇒ 8 - x + 4 + 2x = 0.75 × 20
⇒ x = 15 - 12
⇒ x = 3 kg
∴ 3 kg gold was stolen by the goldsmith.
