Question

State whether ${\text{x% }}$ of $330$ is greater or equal to $330\% $ of ${\text{x}}$? Explain your answer.

Answer 1

Hint: From the given question, we have to show that the given mathematical expressions have either the same value or different value. First, we have to convert the given mathematical expression from percentage to fraction method. Second, we have to know the property of some percentage concept.

Complete step-by-step answer:
From the question, we have to express the given term in fractional form like the above mentioned formula.
Let ${\text{x}}\% $ of $330$ can be expressed in the fractional form as \[\left( {\dfrac{{\text{x}}}{{100}}} \right) \times 330 = \dfrac{{330{\text{x}}}}{{100}}.\]
Let $330\% $ of ${\text{x}}$ can be expressed in the fractional form as \[\left( {\dfrac{{330}}{{100}}} \right) \times {\text{x}} = \dfrac{{330{\text{x}}}}{{100}}.\]
From the above mentioned property of the percentage concept ${\text{x}}\% $ of ${\text{y}}$ is same as ${\text{y}}\% $ of ${\text{x}}$. Therefore the given mathematical expressions ${\text{x}}\% $ of $330$ is the same as $330\% $ of ${\text{x}}$.
$\therefore $ There is no greater value on the comparison of the ${\text{x}}\% $ of $330$ and $330\% $ of ${\text{x}}$. Because the values for both the mathematical expressions are equal on applying the property of the percentage concept.

Therefore the values of both the expressions are equal.

Note: $1.$ If ${\text{x}}\% $ can be expressed in the fractional form as $\dfrac{{\text{x}}}{{100}}$.
$2.$ If ${\text{x}}\% $ of ${\text{y}}$ can be expressed in the fractional form as $\left( {\dfrac{{\text{x}}}{{100}}} \right) \times {\text{y}}$ and then it also can be written as $\dfrac{{{\text{xy}}}}{{100}}$.
$3.$ If ${\text{y}}\% $ of ${\text{x}}$ can be expressed in the fractional form as $\left( {\dfrac{{\text{y}}}{{100}}} \right) \times {\text{x}}$ and then it also can be written as $\dfrac{{{\text{yx}}}}{{100}}$.
From the above point 2 and 3, we understand both the mathematical expressions are equal.
Therefore, the above result can be written as $\dfrac{{{\text{xy}}}}{{100}} = \dfrac{{{\text{yx}}}}{{100}}.$
$\therefore $ ${\text{x}}\% $ of ${\text{y}}$ is same as ${\text{y}}\% $ of ${\text{x}}$.