Question

: The percentage of impurity in the $23$ carat gold is:

Answer 1

Hint: As the pure gold is the $24$ carat gold and to find the impurity of $23$ carat gold first we will find the percentage of purity of given $23$ carat gold (which will be the division of $23$ carat gold with the $24$ carat gold) and then we will subtract result from hundred.

Complete step by step answer:
As we know that the ‘carat’ is used for the measurement of purity of gold that is alloyed with other metals and the $24$ carat gold is considered as $100\% $ pure gold because it is not alloyed with any other metal. The gold which has lower carat value will have lower percentage of gold and higher percentage of other alloyed metal in it and the gold which has higher carat value will have higher percentage of gold and lower percentage of other metal that is alloyed in it.
In the given question, to find the impurity of the $23$ carat gold, we will first find its purity percentage.
As we know that $24$ carat gold has $100\% $ purity
Therefore, $1$ carat gold will have $\dfrac{1}{{24}} \times 100\% $ purity
And now, $23$ carat gold will have $\dfrac{{23}}{{24}} \times 100\% $ purity
Which means $23$ carat gold has $95.834\% $ purity
Now, to find impurity in $23$ carat gold, we will subtract its purity from total percentage.
Therefore, impurity of $23$ carat gold is $ = 100 - 95.834\% $

Hence, impurity of $23$ carat gold is $4.167\% $.

Additional information:
The high end jewellery is often of $18$ carat gold which consists of $75\% $ of pure gold and $25\% $ of copper, silver or many other metals and the low end jewellery is usually of $9$ carat gold which contains $37.5\% $ of pure gold and $62.5\% $ of other metals in it.

Note:
Remember that the pure gold that is $24$ carat gold is very soft due to which it is not suitable for making jewellery therefore, gold is alloyed with a small amount of copper to make the jewellery which makes it hard.