Anurag made a profit of 12% by selling a shirt after a discount of 21 %. If the marked price of the shirt is Rs.6720, find its cost price?

Options

A. Rs. 4740
B. Rs. 4800
C. Rs. 5070
D. Rs. 3940

Answer

To find the cost price of the shirt, we can follow these steps:

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 6720
- Discount = 21%
- Profit = 12%

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

\[ \text{Selling Price (SP)} = \text{Marked Price} \times \left(1 - \frac{\text{Discount}}{100}\right) \]

Substituting the values:

\[ \text{SP} = 6720 \times \left(1 - \frac{21}{100}\right) = 6720 \times 0.79 \]

Calculating the SP:

\[ \text{SP} = 6720 \times 0.79 = 5308.8 \]

### Step 3: Relate Selling Price to Cost Price
We know that:

\[ \text{Selling Price (SP)} = \text{Cost Price (CP)} + \text{Profit} \]

Since the profit is 12% of the cost price, we can express this as:

\[ \text{Profit} = \frac{12}{100} \times \text{CP} \]

Thus, we can rewrite the equation:

\[ 5308.8 = \text{CP} + \frac{12}{100} \times \text{CP} \]

This simplifies to:

\[ 5308.8 = \text{CP} \left(1 + \frac{12}{100}\right) = \text{CP} \times \frac{112}{100} \]

### Step 4: Solve for Cost Price (CP)
Now, we can isolate CP:

\[ \text{CP} = \frac{5308.8 \times 100}{112} \]

Calculating CP:

\[ \text{CP} = \frac{530880}{112} = 4740 \]

Thus, the cost price of the shirt is **Rs. 4740**.

### Summary of Steps:
1. Identify the marked price, discount, and profit.
2. Calculate the selling price after applying the discount.
3. Relate the selling price to the cost price using the profit percentage.
4. Solve for the cost price.