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

Options

A. Rs. 800
B. Rs. 900
C. Rs. 1000
D. Rs. 1100

Answer

To solve the problem step by step, we need to find the marked price (MP) of an article that costs the shopkeeper Rs. 900, so that he can gain a profit of 10% after giving a discount of 10% on the marked price.

### Step 1: Calculate the Selling Price (SP) for a 10% Profit
First, we need to find out what the selling price (SP) should be to achieve a profit of 10% on the cost price (CP).

- **Cost Price (CP)** = Rs. 900
- **Profit Percentage** = 10%

To find the selling price:
\[ SP = CP + \left(\frac{Profit \%}{100} \times CP\right) \]
\[ SP = 900 + \left(\frac{10}{100} \times 900\right) \]
\[ SP = 900 + 90 = Rs. 990 \]

### Step 2: Relate Selling Price to Marked Price and Discount
The shopkeeper sells the goods at a 10% discount on the marked price (MP). This means:
\[ SP = MP - \left(\frac{Discount \%}{100} \times MP\right) \]
Given that the discount is 10%, we can rewrite this as:
\[ SP = MP - \left(\frac{10}{100} \times MP\right) \]
\[ SP = MP \left(1 - \frac{10}{100}\right) \]
\[ SP = MP \left(\frac{90}{100}\right) \]
\[ SP = 0.9 \times MP \]

### Step 3: Substitute the Selling Price to Find Marked Price
Now, we can substitute the selling price we calculated in Step 1 into this equation:
\[ 990 = 0.9 \times MP \]

To find MP, divide both sides by 0.9:
\[ MP = \frac{990}{0.9} \]
\[ MP = 1100 \]

### Final Answer
The marked price (MP) that should be set on the article is **Rs. 1100**.

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