A dealer purchaed an article for Rs. 900 fixes the list price in such a way that he gains 20% after allowing 10% discount, then the list price is :

Options

A. Rs. 1180
B. Rs. 1080
C. Rs. 1200
D. RS. 1100

Answer

To find the list price of the article, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Cost Price (CP)**:
The dealer purchased the article for Rs. 900.
\[ \text{CP} = 900 \]

2. **Calculate the Selling Price (SP)**:
The dealer wants to gain 20% on the cost price. To find the selling price, we calculate 20% of the cost price and add it to the cost price.
\[ \text{Gain} = 20\% \text{ of } \text{CP} = \frac{20}{100} \times 900 = 180 \]
\[ \text{SP} = \text{CP} + \text{Gain} = 900 + 180 = 1080 \]

3. **Determine the List Price (LP)**:
The dealer allows a discount of 10% on the list price. If the list price is denoted as LP, then after allowing a 10% discount, the selling price can be expressed as:
\[ \text{SP} = \text{LP} - 10\% \text{ of } \text{LP} = \text{LP} \times (1 - 0.10) = \text{LP} \times 0.90 \]
Therefore, we can write:
\[ 1080 = \text{LP} \times 0.90 \]

4. **Solve for the List Price (LP)**:
To find the list price, we rearrange the equation:
\[ \text{LP} = \frac{1080}{0.90} \]
Now, calculate the value:
\[ \text{LP} = \frac{1080 \times 100}{90} = \frac{108000}{90} = 1200 \]

Thus, the list price of the article is Rs. 1200.

### Final Answer:
\[ \text{List Price (LP)} = 1200 \]