The marked price of an article is Rs 1200 and discount offered is 31%. If profit is 15%, then what will be the cost price?

Options

A. A) Rs 640
B. B) Rs 704
C. C) Rs 748
D. D) Rs 720

Answer

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

### Step 1: Calculate the Selling Price (SP)
The selling price can be calculated using the formula:
\[ SP = MP \times \left(1 - \frac{D}{100}\right) \]
Where:
- \( MP \) = Marked Price = Rs 1200
- \( D \) = Discount = 31%

Substituting the values:
\[ SP = 1200 \times \left(1 - \frac{31}{100}\right) \]
\[ SP = 1200 \times \left(1 - 0.31\right) \]
\[ SP = 1200 \times 0.69 \]
\[ SP = 828 \]

### Step 2: Relate Selling Price to Cost Price
We know that the selling price can also be expressed in terms of cost price (CP) and profit percentage (P):
\[ SP = CP \times \left(1 + \frac{P}{100}\right) \]
Where:
- \( P \) = Profit = 15%

Substituting the values:
\[ 828 = CP \times \left(1 + \frac{15}{100}\right) \]
\[ 828 = CP \times \left(1 + 0.15\right) \]
\[ 828 = CP \times 1.15 \]

### Step 3: Solve for Cost Price (CP)
To find the cost price, rearrange the equation:
\[ CP = \frac{828}{1.15} \]

Calculating the cost price:
\[ CP = 720 \]

### Final Answer
The cost price of the article is Rs 720.

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