An article listed at Rs. 800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price ?

Options

A. Rs. 620
B. Rs. 600
C. Rs. 640
D. Rs. 680

Answer

To solve the problem step by step, we need to follow these calculations:

### Step 1: Calculate the Selling Price after Successive Discounts
The article is listed at Rs. 800 and is sold at successive discounts of 25% and 15%.

1. **First Discount (25%)**:
\[ \text{Selling Price after 1st Discount} = \text{List Price} \times (1 - \text{Discount Rate}) \]
\[ = 800 \times (1 - 0.25) = 800 \times 0.75 = 600 \]

2. **Second Discount (15%)**:
\[ \text{Selling Price after 2nd Discount} = \text{Selling Price after 1st Discount} \times (1 - \text{Discount Rate}) \]
\[ = 600 \times (1 - 0.15) = 600 \times 0.85 = 510 \]

### Step 2: Determine the Cost Price
The Selling Price after the two discounts is Rs. 510, which is the cost price (CP) for the buyer.

### Step 3: Calculate the Desired Selling Price for a Profit of 20%
The buyer wants to sell the article at a profit of 20% after allowing a 10% discount.

1. **Calculate the Selling Price before Discount**:
\[ \text{Selling Price (SP)} = \text{Cost Price} \times (1 + \text{Profit Rate}) \]
\[ = 510 \times (1 + 0.20) = 510 \times 1.20 = 612 \]

### Step 4: Calculate the List Price
The buyer allows a 10% discount on the list price (LP) to achieve the selling price of Rs. 612.

1. **Using the formula for Selling Price after Discount**:
\[ \text{Selling Price} = \text{List Price} \times (1 - \text{Discount Rate}) \]
\[ 612 = \text{List Price} \times (1 - 0.10) \]
\[ 612 = \text{List Price} \times 0.90 \]

2. **Solving for List Price**:
\[ \text{List Price} = \frac{612}{0.90} = 680 \]

### Final Answer
The list price the buyer should set is **Rs. 680**.

---