An article is marked at Rs 2.250. By selling it at a discount of 12%, the dealer makes a profit of 10%. Find :
the cost price of the article for the dealer.

Answer

To find the cost price of the article for the dealer, we will follow these steps:

### Step 1: Calculate the Discount
The discount is given as 12% of the marked price. The marked price (MP) is Rs 2250.

\[ \text{Discount} = \frac{12}{100} \times 2250 = 270 \]

### Step 2: Calculate the Selling Price
The selling price (SP) can be calculated by subtracting the discount from the marked price.

\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 2250 - 270 = 1980 \]

### Step 3: Use the Profit Formula
We know that the dealer makes a profit of 10%. The formula for profit percentage is:

\[ \text{Profit Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]

Given that the profit percentage is 10%, we can set up the equation:

\[ 10 = \frac{1980 - \text{CP}}{\text{CP}} \times 100 \]

### Step 4: Rearranging the Equation
To solve for the cost price (CP), we rearrange the equation:

\[ 10 = \frac{1980 - \text{CP}}{\text{CP}} \times 100 \]

Dividing both sides by 100:

\[ 0.1 = \frac{1980 - \text{CP}}{\text{CP}} \]

Cross-multiplying gives us:

\[ 0.1 \times \text{CP} = 1980 - \text{CP} \]

### Step 5: Solve for CP
Now, we will add CP to both sides:

\[ 0.1 \text{CP} + \text{CP} = 1980 \]

This simplifies to:

\[ 1.1 \text{CP} = 1980 \]

Now, divide both sides by 1.1:

\[ \text{CP} = \frac{1980}{1.1} = 1800 \]

### Conclusion
The cost price of the article for the dealer is Rs 1800.

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