A shopkeeper marks the price of an article at Rs. 320. Find the cost price if after allowing a discount of `10%` he still gains `20%` on the cost price.
a. Rs. 240
B. Rs. 280
C. Rs. 300
D. Rs. 264

Options

A. A
B. C
C. B
D. D

Answer

To solve the problem step by step, we will use the information provided about the marked price, discount, and profit percentages.

### Step 1: Understand the given information
- Marked Price (MP) = Rs. 320
- Discount = 10%
- Profit = 20%

### Step 2: Calculate the Selling Price (SP)
The Selling Price can be calculated using the formula:
\[ \text{Selling Price (SP)} = \text{Marked Price (MP)} - \text{Discount} \]

First, we calculate the amount of discount:
\[ \text{Discount} = \frac{10}{100} \times 320 = 32 \]

Now, we can find the Selling Price:
\[ \text{SP} = 320 - 32 = 288 \]

### Step 3: Relate Selling Price to Cost Price
We know that the Selling Price is also related to the Cost Price (CP) through the profit percentage. The formula for Selling Price in terms of Cost Price is:
\[ \text{SP} = \text{Cost Price (CP)} + \text{Profit} \]

Since profit is given as 20% of the Cost Price, we can express it 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 4: Set up the equation
Now we can set up the equation using the Selling Price we calculated:
\[ 288 = 1.2 \times \text{CP} \]

### Step 5: Solve for Cost Price
To find the Cost Price, we rearrange the equation:
\[ \text{CP} = \frac{288}{1.2} \]

Calculating this gives:
\[ \text{CP} = 240 \]

### Conclusion
The Cost Price of the article is Rs. 240.

### Answer
The correct option is A. Rs. 240.

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