shopkeeper marks his good at a price such that after giving a discount of 25%, the gains 20%. If the marked price of 44 the article is 736, what is the cost price of the article?

Options

A. Rs. 450
B. Rs. 455
C. Rs. 460
D. Rs. 440

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the given information
- The marked price (MP) of the article is 736.
- The discount given is 25%.
- The profit gained after the discount is 20%.

### Step 2: Calculate the discount amount
To find the discount amount, we can use the formula:
\[ \text{Discount} = \text{Marked Price} \times \frac{\text{Discount Percentage}}{100} \]

Substituting the values:
\[ \text{Discount} = 736 \times \frac{25}{100} = 736 \times 0.25 = 184 \]

### Step 3: Calculate the selling price (SP)
The selling price can be calculated by subtracting the discount from the marked price:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} \]
\[ \text{Selling Price} = 736 - 184 = 552 \]

### Step 4: Relate selling price to cost price
We know that the selling price is also related to the cost price (CP) through the profit percentage. Since the profit is 20%, we can express the selling price as:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
\[ \text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{20}{100}\right) \]
\[ \text{Selling Price} = \text{Cost Price} \times 1.2 \]

### Step 5: Solve for the cost price
Now, substituting the selling price we calculated:
\[ 552 = \text{Cost Price} \times 1.2 \]

To find the cost price, rearranging gives:
\[ \text{Cost Price} = \frac{552}{1.2} \]

Calculating this:
\[ \text{Cost Price} = \frac{5520}{12} = 460 \]

### Final Answer
The cost price of the article is **460**.

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