A profit of 20% is made after giving a discount of 15% on an article. If the marked price of the article is Rs 2760, then what is its cost price (in Rs)?

Options

A. 1955
B. 2150
C. 1845
D. 1890

Answer

To find the cost price of the article given the marked price and the profit percentage after a discount, we can follow these steps:

### Step 1: Calculate the Selling Price after Discount
The marked price (MP) of the article is Rs 2760, and there is a discount of 15%.

To find the selling price (SP) after the discount:
\[ \text{SP} = \text{MP} - \text{Discount} \]
The discount can be calculated as:
\[ \text{Discount} = \frac{15}{100} \times \text{MP} = \frac{15}{100} \times 2760 = 414 \]
Now, substituting the discount back into the selling price formula:
\[ \text{SP} = 2760 - 414 = 2346 \]

### Step 2: Relate Selling Price to Cost Price
We know that the selling price is also related to the cost price (CP) through the profit percentage. Given that there is a profit of 20%, we can express this as:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where profit can be expressed as:
\[ \text{Profit} = \frac{20}{100} \times \text{CP} = 0.2 \times \text{CP} \]
Thus, we can rewrite the selling price equation as:
\[ \text{SP} = \text{CP} + 0.2 \times \text{CP} = 1.2 \times \text{CP} \]

### Step 3: Solve for Cost Price
Now we can set the selling price equal to the expression involving the cost price:
\[ 2346 = 1.2 \times \text{CP} \]
To find the cost price, we rearrange the equation:
\[ \text{CP} = \frac{2346}{1.2} \]
Calculating this gives:
\[ \text{CP} = 1955 \]

### Final Answer
The cost price of the article is Rs 1955.

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