The marked price of an article is Rs. 200. A discount of `12(1)/(2)%` is allowed on the marked price and a profit of `25%` is made. What is the cost price of the article ?

Options

A. Rs. 120
B. Rs. 140
C. Rs. 160
D. Rs. 180

Answer

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

### Step 1: Calculate the Discount Amount
The marked price (MP) of the article is Rs. 200, and the discount is 12.5%.

To calculate the discount amount:
\[ \text{Discount} = \text{Marked Price} \times \left(\frac{\text{Discount Percentage}}{100}\right) \]
\[ \text{Discount} = 200 \times \left(\frac{12.5}{100}\right) = 200 \times 0.125 = 25 \]

### Step 2: Calculate the Selling Price
The selling price (SP) can be calculated by subtracting the discount from the marked price:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]
\[ \text{Selling Price} = 200 - 25 = 175 \]

### Step 3: Calculate the Cost Price
We know that the selling price is also related to the cost price (CP) through the profit percentage. Given that the profit is 25%, we can express the selling price in terms of the cost price:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
\[ \text{Profit} = \text{Cost Price} \times \left(\frac{25}{100}\right) = 0.25 \times \text{Cost Price} \]
Thus,
\[ \text{Selling Price} = \text{Cost Price} + 0.25 \times \text{Cost Price} = 1.25 \times \text{Cost Price} \]
Now, we can substitute the selling price we calculated:
\[ 175 = 1.25 \times \text{Cost Price} \]

### Step 4: Solve for Cost Price
To find the cost price, we can rearrange the equation:
\[ \text{Cost Price} = \frac{175}{1.25} \]
Calculating this gives:
\[ \text{Cost Price} = 140 \]

### Final Answer
The cost price of the article is Rs. 140.

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