Question

What percent of 48 is 30?

Answer 1

Hint: To find what percent of 48 is 30, we have to assume this percentage as x. Then we have to write the given condition as $x\%\text{ of }48=30$ . Then we have to express this form in the mathematical one and solve for x.

Complete step by step solution:
We have to find what percentage of 48 is 30. Let us consider this percentage as x. Hence, we can rewrite the given condition as
$x\%\text{ of }48=30$
Let us express the above in the mathematical form.
$\Rightarrow x\%\times 48=30$
Now, we have to convert x% into its number. We know that a percentage is converted into its number form by dividing the percentage number by 100.
$\Rightarrow \dfrac{x}{100}\times 48=30$
Now, we have to solve for x. For this, let us take 48 from the LHS to the RHS.
$\Rightarrow \dfrac{x}{100}=\dfrac{30}{48}$
Let us take 100 from the LHS to the RHS.
$\Rightarrow x=\dfrac{30\times 100}{48}$
Let us cancel the common factors from the RHS.
\[\begin{align}
  & \Rightarrow x=\dfrac{{{\require{cancel}\cancel{30}}^{5}}\times 100}{{{\require{cancel}\cancel{48}}^{8}}} \\
 & \Rightarrow x=\dfrac{5\times 100}{8} \\
\end{align}\]
We can further simplify the above equation by cancelling the common factor4.
\[\Rightarrow x=\dfrac{5\times {{\require{cancel}\cancel{100}}^{25}}}{{{\require{cancel}\cancel{8}}^{2}}}\]
We can write the simplified form of the above expression as
\[\Rightarrow x=\dfrac{5\times 25}{2}\]
Let us multiply the terms in the numerator of the LHS.
\[\Rightarrow x=\dfrac{125}{2}\]
We have to divide 125 by 2 and find its decimal form.
\[\Rightarrow x=62.5\]
Therefore, 62.5% of 48 is 30.

Note: Students must know how to convert a percentage into a number and vise-versa. They must know that ‘of’ in this question means multiplication. They must also know to solve algebraic expressions.