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 under water gold loses $\frac{1}{20}$th of its weight, while silver loses $\frac{1}{10}$th. When the crown was weighed under water, it was 9.25 kg. How much gold was stolen by the goldsmith?
1 kg
2 kg
3 kg
4 kg
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2018
Let ‘x’ kg of gold be stolen and replaced by ‘x’ kg of silver.
Final composition: (8-x) kg gold, (2+x) kg silver. Total weight is (8-x) + (2+x) = 10 kg.
Under water, gold loses 1/20th of its weight, so its apparent weight is (1 – 1/20) = 19/20 of its actual weight.
Under water, silver loses 1/10th of its weight, so its apparent weight is (1 – 1/10) = 9/10 of its actual weight.
The crown weighs 9.25 kg under water.
Apparent weight of gold = (19/20) * (8-x)
Apparent weight of silver = (9/10) * (2+x)
Total apparent weight = (19/20) * (8-x) + (9/10) * (2+x) = 9.25
Multiply by 20 to clear the denominators:
19 * (8-x) + 18 * (2+x) = 9.25 * 20
152 – 19x + 36 + 18x = 185
188 – x = 185
x = 188 – 185
x = 3 kg.
The goldsmith stole 3 kg of gold.