A shopkeeper sells his goods at 10% discount on the marked price. What price should he mark on an article that costs him Rs. 900 to gain 10% ?

Options

A. Rs. 1275
B. Rs. 1250
C. Rs. 1175
D. Rs. 1100

Answer

To solve the problem step by step, we need to find the marked price (MP) that the shopkeeper should set in order to achieve a 10% profit on an article that costs him Rs. 900, while also applying a 10% discount on the marked price.

### Step 1: Determine the Cost Price (CP) and Selling Price (SP)
- The cost price (CP) of the article is given as Rs. 900.
- To gain a profit of 10%, we need to calculate the selling price (SP).
- The formula for SP when there is a profit is:
\[ SP = CP + \text{Profit} \]
- The profit can be calculated as:
\[ \text{Profit} = \frac{10}{100} \times CP = \frac{10}{100} \times 900 = 90 \]
- Therefore, the selling price (SP) is:
\[ SP = 900 + 90 = 990 \]

### Step 2: Relate Selling Price to Marked Price
- The shopkeeper sells the goods at a 10% discount on the marked price (MP).
- This means that the selling price (SP) is 90% of the marked price (MP), since:
\[ SP = MP - \text{Discount} \]
- The discount is 10% of the marked price, which can be expressed as:
\[ \text{Discount} = \frac{10}{100} \times MP = 0.1 \times MP \]
- Therefore, we can write:
\[ SP = MP - 0.1 \times MP = 0.9 \times MP \]

### Step 3: Set up the equation
- Now we can set up the equation using the SP we calculated:
\[ 990 = 0.9 \times MP \]

### Step 4: Solve for Marked Price (MP)
- To find the marked price (MP), we can rearrange the equation:
\[ MP = \frac{990}{0.9} \]
- Calculating this gives:
\[ MP = 1100 \]

### Conclusion
- The marked price (MP) that the shopkeeper should set is Rs. 1100.