A shopkeeper marks the price of the article in such a way that after allowing 28% discount, he wants a gain of 12%. If the marked price is Rs. 224, then the cost price of the article is:

Options

A. Rs 168
B. Rs 120
C. Rs 144
D. Rs 196

Answer

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

### Step 1: Identify the given values
- Marked Price (MP) = Rs. 224
- Discount = 28%
- Desired Profit = 12%

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

First, we need to calculate the amount of discount:
\[ \text{Discount Amount} = \text{MP} \times \frac{\text{Discount}}{100} = 224 \times \frac{28}{100} = 224 \times 0.28 = Rs. 62.72 \]

Now, we can find the Selling Price:
\[ \text{SP} = \text{MP} - \text{Discount Amount} = 224 - 62.72 = Rs. 161.28 \]

### Step 3: Relate Selling Price to Cost Price
The Selling Price is also related to the Cost Price (CP) and the profit percentage:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where Profit can be expressed as:
\[ \text{Profit} = \text{CP} \times \frac{\text{Profit Percentage}}{100} \]

Given that the profit percentage is 12%, we can express SP as:
\[ \text{SP} = \text{CP} + \text{CP} \times \frac{12}{100} = \text{CP} \times \left(1 + \frac{12}{100}\right) = \text{CP} \times 1.12 \]

### Step 4: Set up the equation
Now we can set up the equation using the Selling Price we calculated:
\[ 161.28 = \text{CP} \times 1.12 \]

### Step 5: Solve for Cost Price (CP)
To find CP, we can rearrange the equation:
\[ \text{CP} = \frac{161.28}{1.12} \]

Calculating this gives:
\[ \text{CP} = 144 \]

### Conclusion
The cost price of the article is Rs. 144.

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