By what percent must a stock price increase to reach its former value after a 20% decrease?

• A. 15%
• B. 20%
• C. 25%
• D. 40%

Answer: (C)

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:

[