Question

A shopkeeper has two types of wheat. The percentage of pure wheat first type of wheat is 80% and the percentage of pure wheat in the second type of wheat is 60%.If he mixes 28kg of first type of wheat to the 32kg of second type of wheat , then find the percentage of pure wheat in resultant wheat in the mixture.

Answer 1

Hint:
Here we are going to find the total weight of the resultant mixture formed by mixing both the wheat and find the total amount of pure wheat in the mixture, and then with the help of it we will finally find the percentage.

Complete step-by-step answer:
It is given that the percentage of pure wheat in the first type of wheat is 80% and the percentage of pure wheat in the second type of wheat is 60%.
Also he mixes 28kg of the first type of wheat to the 32kg of the second type of wheat.
Therefore the weight of the resultant mixture is given by adding the given weights of both the types =28kg+32kg
=60kg
To find the amount of pure wheat in resultant mixture we use the following formula
The amount of pure wheat in resultant mixture =the sum of the pure wheat in first type and second type
Therefore we get,
\[ = 28 \times 80\% + 32 \times 60\% \]
By using the formula of percentage in above equation we get, the above equation as follows,
\[ = 28 \times \dfrac{{80}}{{100}} + 32 \times \dfrac{{60}}{{100}}\]
Let us solve the multiplication and division in the above equation, therefore we get,
\[ = \dfrac{{112}}{5} + \dfrac{{96}}{5}\]
On further solving we get,
The amount of pure wheat in the resultant mixture\[ = \dfrac{{208}}{5} = 41.60kg\]
Therefore the amount of pure wheat in resultant mixture =41.60kg.
Now we have to find the percentage of pure wheat in the resultant mixture it is found using the following formula,
The percentage of pure wheat in resultant wheat in the mixture
\[\;100 \times \dfrac{{Amount{\text{ }}of{\text{ }}pure{\text{ }}wheat{\text{ }}in{\text{ }}resultant{\text{ }}mixture}}{{Total{\text{ }}weight{\text{ }}of{\text{ }}the{\text{ }}resultant{\text{ }}mixture}}\]
By substituting the found values in the above equation we get,
The percentage of pure wheat in resultant wheat in the mixture\[ = \dfrac{{41.60}}{{60}} \times 100\]
\[ = 69.33\% \]
Hence, we have found the percentage of pure wheat in resultant wheat in the mixture is 69.33%.

Note:
The percentage of x is denoted by x% and defined by,
\[x\% = \dfrac{x}{{100}}\]
To find the percentage of one number in relation to another with the formula percentage, we use the following formula
\[\dfrac{{number{\text{ }}you{\text{ }}want{\text{ }}to{\text{ }}find{\text{ }}the{\text{ }}percentage{\text{ }}for}}{{total}} \times 100\]