Answer
Verified
402.3k+ views
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.
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.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Two charges are placed at a certain distance apart class 12 physics CBSE
Difference Between Plant Cell and Animal Cell
What organs are located on the left side of your body class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The planet nearest to earth is A Mercury B Venus C class 6 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is BLO What is the full form of BLO class 8 social science CBSE