If price of a book is first decreased by 25% and then increased by 20%, the net change in the price of the book will be

Options

A. 10% decrease
B. 5% decrease
C. no change
D. 5% Incease

Answer

To solve the problem of finding the net change in the price of a book after a 25% decrease followed by a 20% increase, we can follow these steps:

### Step 1: Define the Original Price
Let's assume the original price of the book is \( P \).

### Step 2: Calculate the Price After the 25% Decrease
A decrease of 25% means we will retain 75% of the original price. Therefore, the new price after the decrease is:
\[ \text{New Price} = P - 0.25P = 0.75P \]

### Step 3: Calculate the Price After the 20% Increase
Now, we need to increase the new price by 20%. The increase of 20% on \( 0.75P \) is:
\[ \text{Increase} = 0.20 \times 0.75P = 0.15P \]
Thus, the price after the increase will be:
\[ \text{Final Price} = 0.75P + 0.15P = 0.90P \]

### Step 4: Determine the Net Change in Price
Now we compare the final price with the original price:
\[ \text{Net Change} = \text{Final Price} - \text{Original Price} = 0.90P - P = -0.10P \]
This indicates a decrease in price.

### Step 5: Calculate the Percentage Change
To find the percentage change, we use the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Net Change}}{\text{Original Price}} \right) \times 100 \]
Substituting in the values:
\[ \text{Percentage Change} = \left( \frac{-0.10P}{P} \right) \times 100 = -10\% \]
This indicates a 10% decrease in the price of the book.

### Conclusion
The net change in the price of the book is a **10% decrease**.

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