A house was sold for Rs. y by giving a discount of x%, then the list price was :

Options

A. `(100 y)/(100-x)`
B. `(100y)/(1-(x)/(100))`
C. `(100x)/(100-y)`
D. `(100y)/(1-x)`

Answer

To find the list price (marked price) of a house sold for Rs. y after giving a discount of x%, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between Selling Price, List Price, and Discount**:
- The selling price (SP) is the price after the discount is applied to the list price (LP).
- The discount can be expressed as a percentage of the list price.

2. **Convert the percentage discount into a fraction**:
- The discount of x% can be written as \( \frac{x}{100} \).

3. **Set up the equation**:
- If the list price is denoted as LP, then the selling price can be calculated as:
\[ SP = LP - \text{Discount} \]
- The discount can be expressed as:
\[ \text{Discount} = \frac{x}{100} \times LP \]
- Therefore, we can rewrite the selling price as:
\[ SP = LP - \frac{x}{100} \times LP = LP \left(1 - \frac{x}{100}\right) \]

4. **Substituting the selling price**:
- Given that the selling price (SP) is Rs. y, we can substitute this into our equation:
\[ y = LP \left(1 - \frac{x}{100}\right) \]

5. **Solve for the List Price (LP)**:
- To find the list price, rearrange the equation:
\[ LP = \frac{y}{1 - \frac{x}{100}} \]
- To simplify further, multiply the numerator and denominator by 100:
\[ LP = \frac{100y}{100 - x} \]

### Final Answer:
The list price (marked price) of the house is:
\[ \text{List Price} = \frac{100y}{100 - x} \]

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