A number is increased by 25 percent and then decreased by 20 percent. The result is what percent of the original number?

Options

A. 80
B. 100
C. 105
D. 120

Answer

Let's solve the problem step by step.

### Step 1: Define the original number
Let the original number be \( x \).

### Step 2: Increase the number by 25%
To increase the number \( x \) by 25%, we calculate:
\[ \text{Increased value} = x + 0.25x = x + \frac{25}{100}x = x + \frac{x}{4} = \frac{4x}{4} + \frac{x}{4} = \frac{5x}{4} \]

### Step 3: Decrease the increased number by 20%
Now, we need to decrease \( \frac{5x}{4} \) by 20%. First, we calculate 20% of \( \frac{5x}{4} \):
\[ \text{Decrease} = 0.20 \times \frac{5x}{4} = \frac{20}{100} \times \frac{5x}{4} = \frac{1}{5} \times \frac{5x}{4} = \frac{5x}{20} = \frac{x}{4} \]
Now, we subtract this decrease from the increased value:
\[ \text{Final value} = \frac{5x}{4} - \frac{x}{4} = \frac{5x - x}{4} = \frac{4x}{4} = x \]

### Step 4: Find what percent the final value is of the original number
The final value is \( x \), which is the same as the original number. To find what percent \( x \) is of \( x \):
\[ \text{Percentage} = \left( \frac{x}{x} \right) \times 100\% = 100\% \]

### Conclusion
The result is \( 100\% \) of the original number.