The list price of an article is Rs 800 and is available at a discount of 15 percent. Find : (1) the selling price of the article, (ii) the cost price of the article, if a profit of `13 (1)/(3) %` is made on selling it.

Answer

To solve the given problem step by step, we will break it down into two parts: finding the selling price and then finding the cost price.

### Step 1: Calculate the Selling Price

1. **Identify the list price and discount percentage**:
- List Price (LP) = Rs 800
- Discount Percentage (D) = 15%

2. **Calculate the discount amount**:
\[ \text{Discount Amount} = \frac{D}{100} \times \text{LP} = \frac{15}{100} \times 800 = 120 \text{ Rs} \]

3. **Calculate the Selling Price (SP)**:
\[ \text{Selling Price} = \text{LP} - \text{Discount Amount} = 800 - 120 = 680 \text{ Rs} \]

### Step 2: Calculate the Cost Price

1. **Identify the profit percentage**:
- Profit Percentage (P) = \(13 \frac{1}{3}\% = \frac{40}{3}\%\)

2. **Convert profit percentage to decimal**:
\[ P = \frac{40}{3} \div 100 = \frac{40}{300} = \frac{2}{15} \]

3. **Use the formula for Selling Price in terms of Cost Price (CP)**:
\[ \text{SP} = \text{CP} + \text{Profit} \]
\[ \text{SP} = \text{CP} + \left(\frac{P}{100} \times \text{CP}\right) \]
\[ \text{SP} = \text{CP} \left(1 + \frac{P}{100}\right) \]

4. **Rearranging the formula to find Cost Price**:
\[ \text{CP} = \frac{\text{SP}}{1 + \frac{P}{100}} = \frac{680}{1 + \frac{40}{300}} = \frac{680}{1 + \frac{2}{15}} = \frac{680}{\frac{17}{15}} = 680 \times \frac{15}{17} \]

5. **Calculate the Cost Price**:
\[ \text{CP} = \frac{680 \times 15}{17} = 600 \text{ Rs} \]

### Final Answers:
1. Selling Price = Rs 680
2. Cost Price = Rs 600