Vishakha offers a discount of 20% on all the items at her shop and still makes a profit of 12%. What is the cost price of an article marked at Rs 280?

Answer

To find the cost price of an article marked at Rs 280, with a discount of 20% and a profit of 12%, we can follow these steps:

### Step 1: Calculate the Discount Amount
The discount offered is 20% of the marked price (MP).

\[ \text{Discount} = \frac{20}{100} \times 280 = 56 \]

### Step 2: Calculate the Selling Price
The selling price (SP) is calculated by subtracting the discount from the marked price.

\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = 280 - 56 = 224 \]

### Step 3: Set Up the Profit Equation
Let the cost price (CP) be \( X \). Since Vishakha makes a profit of 12%, the selling price can also be expressed as:

\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]

The profit can be calculated as:

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

Thus, we can write:

\[ 224 = X + \frac{12X}{100} \]

### Step 4: Combine the Terms
To combine the terms, we can express \( X \) in a common denominator:

\[ 224 = \frac{100X + 12X}{100} = \frac{112X}{100} \]

### Step 5: Solve for Cost Price
Now, we can solve for \( X \):

\[ 224 \times 100 = 112X \]
\[ 22400 = 112X \]
\[ X = \frac{22400}{112} = 200 \]

### Conclusion
The cost price of the article is Rs 200.

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