A number is increased by 25%. To obtain the old number, by how much should it be decreased?

Options

A. 15
B. 20
C. 25
D. 18

Answer

To solve the problem step by step, we can follow these calculations:

1. **Define the Original Number**:
Let's denote the original number as \( x \).

2. **Calculate the Increased Number**:
If the original number \( x \) is increased by 25%, the new number can be calculated as:
\[ \text{Increased Number} = x + 0.25x = 1.25x \]

3. **Determine the Decrease Needed to Get Back to the Original Number**:
We need to find out by what percentage we should decrease the increased number \( 1.25x \) to get back to the original number \( x \).

4. **Set Up the Equation**:
Let \( y \) be the percentage decrease needed. The decreased number can be expressed as:
\[ \text{Decreased Number} = 1.25x - \left( \frac{y}{100} \times 1.25x \right) \]
We want this to equal the original number \( x \):
\[ 1.25x - \left( \frac{y}{100} \times 1.25x \right) = x \]

5. **Simplify the Equation**:
Rearranging the equation gives:
\[ 1.25x - x = \frac{y}{100} \times 1.25x \]
\[ 0.25x = \frac{y}{100} \times 1.25x \]

6. **Cancel \( x \) from Both Sides**:
Assuming \( x \neq 0 \), we can divide both sides by \( x \):
\[ 0.25 = \frac{y}{100} \times 1.25 \]

7. **Solve for \( y \)**:
Multiply both sides by 100:
\[ 25 = 1.25y \]
Now, divide both sides by 1.25:
\[ y = \frac{25}{1.25} = 20 \]

8. **Conclusion**:
Therefore, to obtain the old number after a 25% increase, the number should be decreased by **20%**.