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Hint: The constant is based on the concept of proportionality. Let the purity in carat scale be k carat and the corresponding to k the purity in % scale be p%. So, p is proportional to k. Take the constant of proportionality to be c and remove the proportionality sign. Now find c using the statement that 24 carat is 100% pure. Put c and 22 carat in the equation to get % purity.

__Complete step-by-step answer:__

To start with the question, we let the purity in carat scale be k carat and the corresponding to k the purity in % scale be p%.

Let us first try to interpret the question in mathematical terms. We know that the purity in carat scale is directly proportional to the % purity.

$ k\propto p $

Now according to the definition of proportionality, we can represent the above statement as:

$ k=cp $

In the above equation, c is the constant of proportionality.

Now according to the question 24 carat represents 100% purity. Representing it mathematically using the above equation, we get

$ k=cp $

$ \Rightarrow 24=100c $

\[\Rightarrow c=\dfrac{24}{100}\text{ }..........\text{(i)}\]

Therefore, the value of the constant of proportionality is $ \dfrac{24}{100} $ .

We will now find the purity corresponding to 22 carats.

$ k=cp $

On substituting the value of c from equation (i), we get

$ k=\dfrac{24}{100}\times p $

$ \Rightarrow 22=\dfrac{24}{100}\times p $

$ \Rightarrow 22\times \dfrac{100}{24}=p $

$ \Rightarrow p=91.66% $

Therefore, the answer to the above question is 91.66%.

Note: In the question related to proportionality, the key thing is to find the constant of proportionality. Also, the other important thing is the calculation part, which might be a bit complex due to decimal calculations, so be careful while calculating.

To start with the question, we let the purity in carat scale be k carat and the corresponding to k the purity in % scale be p%.

Let us first try to interpret the question in mathematical terms. We know that the purity in carat scale is directly proportional to the % purity.

$ k\propto p $

Now according to the definition of proportionality, we can represent the above statement as:

$ k=cp $

In the above equation, c is the constant of proportionality.

Now according to the question 24 carat represents 100% purity. Representing it mathematically using the above equation, we get

$ k=cp $

$ \Rightarrow 24=100c $

\[\Rightarrow c=\dfrac{24}{100}\text{ }..........\text{(i)}\]

Therefore, the value of the constant of proportionality is $ \dfrac{24}{100} $ .

We will now find the purity corresponding to 22 carats.

$ k=cp $

On substituting the value of c from equation (i), we get

$ k=\dfrac{24}{100}\times p $

$ \Rightarrow 22=\dfrac{24}{100}\times p $

$ \Rightarrow 22\times \dfrac{100}{24}=p $

$ \Rightarrow p=91.66% $

Therefore, the answer to the above question is 91.66%.

Note: In the question related to proportionality, the key thing is to find the constant of proportionality. Also, the other important thing is the calculation part, which might be a bit complex due to decimal calculations, so be careful while calculating.

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