An article is listed at Rs. 900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single dicount of 16% instead of two discounts ?

Options

A. Gain of Rs. 4.76
B. Loss of Rs. 5.76
C. Gain of Rs. 5.76
D. Loss of Rs. 4.76

Answer

To solve the problem, we need to calculate the selling price of the article after applying two successive discounts of 8% each, and then compare it with the selling price after applying a single discount of 16%. Finally, we will determine if there is a gain or loss.

### Step-by-Step Solution:

1. **Calculate the Selling Price after Two Successive Discounts of 8%:**
- The listed price of the article = Rs. 900.
- First discount = 8% of Rs. 900.
\[ \text{First Discount} = \frac{8}{100} \times 900 = 72 \]
- Selling price after the first discount:
\[ \text{Selling Price after 1st Discount} = 900 - 72 = 828 \]
- Second discount = 8% of Rs. 828.
\[ \text{Second Discount} = \frac{8}{100} \times 828 = 66.24 \]
- Selling price after the second discount:
\[ \text{Selling Price after 2nd Discount} = 828 - 66.24 = 761.76 \]

2. **Calculate the Selling Price after a Single Discount of 16%:**
- Single discount = 16% of Rs. 900.
\[ \text{Single Discount} = \frac{16}{100} \times 900 = 144 \]
- Selling price after single discount:
\[ \text{Selling Price after Single Discount} = 900 - 144 = 756 \]

3. **Determine Gain or Loss:**
- Selling price after two successive discounts = Rs. 761.76.
- Selling price after single discount = Rs. 756.
- To find the gain or loss:
\[ \text{Gain or Loss} = \text{Selling Price after 2nd Discount} - \text{Selling Price after Single Discount} \]
\[ \text{Gain or Loss} = 761.76 - 756 = 5.76 \]
- Since the result is positive, it indicates a gain.

### Final Answer:
The seller would gain Rs. 5.76 if he gives a single discount of 16% instead of two successive discounts of 8%.