An itam is discouned by `20%` and then a `20%` surcharge is applied to the discouned price.
`{:("Quantity A","Quantity B"),("The price after the","The original price"),("discount and surcharge",):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we will follow these steps:

1. **Assume the Original Price**: Let's assume the original price of the item is \( P = 100 \) (this can be any convenient amount, but using 100 makes calculations easier).

2. **Calculate the Discount**: The item is discounted by \( 20\% \). To find the discount amount:
\[ \text{Discount} = 20\% \text{ of } P = \frac{20}{100} \times 100 = 20 \]

3. **Calculate the Price After Discount**: Subtract the discount from the original price:
\[ \text{Price after Discount} = P - \text{Discount} = 100 - 20 = 80 \]

4. **Calculate the Surcharge**: A \( 20\% \) surcharge is then applied to the discounted price. To find the surcharge amount:
\[ \text{Surcharge} = 20\% \text{ of } \text{Price after Discount} = \frac{20}{100} \times 80 = 16 \]

5. **Calculate the Final Price After Surcharge**: Add the surcharge to the discounted price:
\[ \text{Final Price} = \text{Price after Discount} + \text{Surcharge} = 80 + 16 = 96 \]

6. **Compare Quantity A and Quantity B**:
- Quantity A (Price after discount and surcharge) = 96
- Quantity B (Original Price) = 100

Thus, we can conclude:
\[ \text{Quantity B} > \text{Quantity A} \]

### Final Conclusion:
The original price (Quantity B) is greater than the price after the discount and surcharge (Quantity A).