Question

Find the percentage of pure gold in $$22$$ carat gold. If $$24$$ carat gold is $$100\mathrm{\%}$$.

Answer 1

Hint: We need to calculate how much part it is over the original portion of the given material.
Divide the part of gold in an impurity mixture by the part of gold in pure gold.
And, then multiply it by $$100$$.
Finally we get the required answer.

Formula used: If $$a$$ is smaller than $$b$$ then we can say that $$a$$is $$\left({\displaystyle \frac{a}{b}}\right)$$ part of $$b$$, which makes that $$\left(\left({\displaystyle \frac{a}{b}}\right)\times 100\right)\mathrm{\%}$$ of $$b$$.
So, the smaller part will be in the numerator and the larger part will be in the denominator part in the fraction.

Complete step-by-step solution:
It is given in the question that $$100\mathrm{\%}$$ gold means that it is $$24$$ carat gold.
It states that $$24$$ carat gold does not have any impurities.
So, $$22$$ carat gold means that it has $$22$$ part pure gold and $$2$$ part impurities in the formed metal.
So, if we divide $$22$$ by $$24$$ and then multiply it by $$100$$, it will give us the percentage value of gold that is present in the formed metal.
In the following picture we can show the part of impurities:

So, pure gold present in $$22$$ carat gold is $$={\displaystyle \frac{22}{24}}$$ part of $$24$$ carat gold.
Here is the calculation part, $${\displaystyle \frac{22}{24}}$$
On divide numerator and denominator by $$2$$
$$={\displaystyle \frac{11}{12}}$$
Let us divide the term and we get
$$=0.9167$$.
If we multiply the above result by $$100$$, then we will get the percentage value of pure gold present in $$22$$ carat gold.
So, the percentage of pure gold present in $$22$$ carat gold is $$\Rightarrow 0.9167\times 100$$
Let us multiply the terms and we get
$$=91.67\mathrm{\%}$$
$$\therefore$$ The required answer is $$91.67\mathrm{\%}$$.

Note: A percentage is a dimensionless number and it has no unit of measurement.
Always remember that a percentage is a ratio of a number to $$100$$.