Answer

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**Hint:**To solve this question, we will use the concept of percentage and ratio. What we will do is firstly we will find the percentage of gold in 1 carat of gold, by using the relation given in question. After that, we will solve for the percentage of 22 carats of gold by multiplying to the value of gold in 1 carat.

**Complete step by step answer:**

Now, firstly let us find out how much percent of gold is in 1 carat of gold.

In question it is given that 24 carats of gold is 100% pure.

So, we can say that, 24 carat gold = 100

Now, we have to calculate the amount of gold in 1 carat.

So, dividing the equality by 24 on both sides, we get

$\dfrac{24}{24}=\dfrac{100}{24}\%$

$1=\dfrac{100}{24}\%$

So, we get that in 1 carat of gold there is $\dfrac{100}{24}\%$ of gold.

Now in question we are asked to calculate the percentage of gold in 22 carats of gold.

So, multiplying the equality $1=\dfrac{100}{24}\%$ by 22 on both sides, we get

$22\times 1=\dfrac{22}{24}\times 100\%$

On simplifying the equation, we get

$22=\dfrac{11}{12}\times 100\%$

On solving, we get

$22=91\dfrac{2}{3}\%$

Which is approximately equals to 91.66%

**So, 22 carats of gold is 91.66% pure.**

**Note:**To do such questions, always remember that when we calculate for smaller proportion from the larger proportion, we divide the values and we calculate larger proportion from smaller proportion we multiply the values. Also, always remember that $Percentage=\dfrac{\text{Considered Amount}}{\text{Actual Amount}}\times 100$ . Try not to do any calculation error or mistake while doing solution to get an accurate and correct answer.

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