A retailer sold a suit for Rs.8,832 after allowing 8% discount on marked price and further 4% cash discount. If he made 38% profit, find the cost price and the marked price of the suit.

Answer

To solve the problem step by step, we will find the marked price and the cost price of the suit based on the information provided.

### Step 1: Let the marked price of the suit be \( X \).
- **Hint**: Start by defining the variable for the marked price, which is the original price before any discounts.

### Step 2: Calculate the selling price after the 8% discount on the marked price.
- The discount is 8% of \( X \), which is \( 0.08X \).
- Therefore, the price after the 8% discount is:
\[ \text{Price after discount} = X - 0.08X = 0.92X \]
- **Hint**: Remember that subtracting the discount from the marked price gives you the price after the discount.

### Step 3: Calculate the cash discount of 4% on the discounted price.
- The cash discount is 4% of \( 0.92X \), which is:
\[ \text{Cash discount} = 0.04 \times 0.92X = 0.0368X \]
- **Hint**: To find the cash discount, multiply the discounted price by the cash discount percentage.

### Step 4: Determine the final selling price after applying the cash discount.
- The selling price after the cash discount is:
\[ \text{Selling Price} = 0.92X - 0.0368X = 0.8832X \]
- **Hint**: Subtract the cash discount from the price after the first discount to find the final selling price.

### Step 5: Set the selling price equal to Rs. 8,832.
- From the problem, we know that the selling price is Rs. 8,832:
\[ 0.8832X = 8832 \]
- **Hint**: This equation allows you to solve for the marked price \( X \).

### Step 6: Solve for \( X \) (the marked price).
- Rearranging the equation gives:
\[ X = \frac{8832}{0.8832} = 10000 \]
- **Hint**: When dividing, ensure you perform the calculation accurately to find the marked price.

### Step 7: Now, let the cost price be \( Y \).
- **Hint**: Define another variable for the cost price to proceed with the profit calculation.

### Step 8: Calculate the selling price in terms of the cost price and profit.
- The profit is given as 38% of the cost price:
\[ \text{Profit} = 0.38Y \]
- Therefore, the selling price can be expressed as:
\[ \text{Selling Price} = Y + 0.38Y = 1.38Y \]
- **Hint**: Profit is added to the cost price to find the selling price.

### Step 9: Set the selling price equal to Rs. 8,832.
- From the problem, we know:
\[ 1.38Y = 8832 \]
- **Hint**: This equation will help you find the cost price \( Y \).

### Step 10: Solve for \( Y \) (the cost price).
- Rearranging the equation gives:
\[ Y = \frac{8832}{1.38} \approx 6400 \]
- **Hint**: Perform the division carefully to find the cost price.

### Final Answers:
- **Marked Price**: Rs. 10,000
- **Cost Price**: Rs. 6,400