The price of gas increased by 12% per gallon sometime during the first fiscal quarter and then decreased by 25% per gallon by the end of the second fiscal quarter. The final price of gas gallon at the end of the second quarter decreased by what percent compared to the starting price at the beginning of the first fiscal quarter?

Options

A. `13%`
B. `16%`
C. `18.5%`
D. `20%`

Answer

To solve the problem step by step, we will first define the initial price of gas and then apply the percentage changes accordingly.

### Step-by-Step Solution:

1. **Define the Initial Price**:
Let the initial price of gas be \( P \) dollars.

2. **Calculate the Price After the First Increase**:
The price of gas increases by 12%.
To find the new price after the increase:
\[ \text{New Price} = P + 0.12P = P(1 + 0.12) = P \times 1.12 \]

3. **Calculate the Price After the Second Decrease**:
The price then decreases by 25% from the new price.
To find the price after the decrease:
\[ \text{Final Price} = \text{New Price} - 0.25 \times \text{New Price} = \text{New Price} \times (1 - 0.25) = P \times 1.12 \times 0.75 \]
Simplifying this:
\[ \text{Final Price} = P \times 1.12 \times 0.75 = P \times 0.84 \]

4. **Calculate the Overall Change in Price**:
Now, we need to find out how much the final price has decreased compared to the initial price. The decrease in price can be calculated as:
\[ \text{Decrease} = P - \text{Final Price} = P - P \times 0.84 = P(1 - 0.84) = P \times 0.16 \]

5. **Calculate the Percentage Decrease**:
To find the percentage decrease compared to the initial price:
\[ \text{Percentage Decrease} = \left(\frac{\text{Decrease}}{P}\right) \times 100 = \left(\frac{P \times 0.16}{P}\right) \times 100 = 16\% \]

### Conclusion:
The final price of gas at the end of the second quarter decreased by **16%** compared to the starting price at the beginning of the first fiscal quarter.

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