Question

A number increases from $30$ to $40$ and then decreases from $40$ to $30$. Compare the percent of increase from $30$ to $40$ and that of the decrease from $40$ to $30$.

Answer 1

Given that a number increases from $30$ to $40$ and then decreases from $40$ to $30$.

Step 1: Finding the percent of increase from $30$ to $40$

We know that $\mathrm{Increase}\%=\left(\frac{\mathrm{Increase}}{\mathrm{Original}\mathrm{value}}\times 100\right)\%$

Here the original value is $30$ and the increased value is $40-30=10$

$$\begin{gathered} =\left(\frac{10}{30}\times 100\right)\% \\ =\frac{100}{3}\% \\ =33.33\% \end{gathered}$$

Step 2: Finding the percent of decrease from $40$ to $30$

We know that $\mathrm{Decrease}\%=\left(\frac{\mathrm{Decrease}}{\mathrm{Original}\mathrm{value}}\times 100\right)\%$

Here the original value is $40$ and the decreased value is $40-30=10$

$$\begin{gathered} =\left(\frac{10}{40}\times 100\right)\% \\ =\frac{100}{4}\% \\ =25\% \end{gathered}$$the percent decrease is less than the percent increase.

Since $25\%<33.33\%$

Therefore it is clear that the percent of decrease is less than the percent of the increase.