ASVAB Arithmetic Reasoning Practice Test

To find the percentage increase required for a stock price to recover to its previous value after a 20% decrease, it's essential to understand how percentage changes work in reverse.

Let’s denote the original stock price as \( P \). After a 20% decrease, the new price is calculated as:

\[ P - 0.2P = 0.8P \]

Now, to restore the stock price back to its original value, we want to find the percentage increase needed from \( 0.8P \) to \( P \). The increase required is:

\[ P - 0.8P = 0.2P \]

To find the percentage increase relative to the new price (\( 0.8P \)), we use the formula for percentage increase:

\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original Price (after decrease)}} \right) \times 100 \]

Substituting in our values:

\[ \text{Percentage Increase} = \left( \frac{0.2P}{0.8P} \right) \times 100 \]

The \( P \) in the numerator and denominator cancels out:

\[