Question

What is the number whose $20\%$ is $30\%$ of $40$?

Answer 1

Step 1. Find $30\%$ of $40$.

To remove the percentage sign divide the number by 100, replace the word “of” by the multiplication sign and then simplify:

$\begin{array}{rcl}30\%\times 40& =& \frac{30}{100}\times 40\\ & \Rightarrow & 30\%\times 40=12\end{array}$

So, $30\%$ of 40 is 12.

Step 2. Determine a number whose $20\%$ is 12.

Assume that $20\%$ of x is 12. Form an equation as done in step 1 and simplify:

$\begin{array}{rcl}20\%\times x& =& 12\\ & \Rightarrow & \frac{20}{100}\times x=12\\ & \Rightarrow & x=\frac{1200}{20}\\ & \Rightarrow & x=60\end{array}$

Hence, the required number is $60.$