A price is increased by 16.66%. To obtain the old price, by how much should it be decreased?

Options

A. 14.28
B. 16.66
C. 30
D. 33.32

Answer

To solve the problem of how much a price should be decreased to revert to its original value after a 16.66% increase, we can follow these steps:

### Step-by-Step Solution:

1. **Assume an Original Price**:
Let's assume the original price (old price) is \( P = 100 \).

2. **Calculate the Increase**:
The price is increased by 16.66%. To find the amount of increase:
\[ \text{Increase} = P \times \frac{16.66}{100} = 100 \times 0.1666 = 16.66 \]

3. **Calculate the New Price**:
Now, we add the increase to the original price to find the new price:
\[ \text{New Price} = P + \text{Increase} = 100 + 16.66 = 116.66 \]

4. **Determine the Decrease Required**:
To revert to the old price, we need to find out how much we need to decrease the new price:
\[ \text{Decrease} = \text{New Price} - \text{Old Price} = 116.66 - 100 = 16.66 \]

5. **Calculate the Percentage Decrease**:
To find the percentage decrease based on the new price:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease}}{\text{New Price}} \right) \times 100 = \left( \frac{16.66}{116.66} \right) \times 100 \]
\[ \text{Percentage Decrease} = \left( 0.1428 \right) \times 100 \approx 14.28\% \]

### Final Answer:
The price should be decreased by approximately **14.28%** to revert to the old price.