A shopkeeper buys an article for Rs 360. He wants to make a gain of 25% on it after a discount of 10%. The marked price is

Options

A. Rs. 486
B. Rs. 450
C. Rs. 500
D. Rs. 460

Answer

To find the marked price (MP) of the article, we can follow these steps:

### Step 1: Determine the Cost Price (CP) and the Desired Selling Price (SP)
The shopkeeper buys the article for Rs 360. He wants to make a gain of 25%.
To find the Selling Price (SP), we can use the formula:
\[ SP = CP + \text{Gain} \]
Where Gain is 25% of CP.

First, we calculate the gain:
\[ \text{Gain} = 25\% \text{ of } 360 = \frac{25}{100} \times 360 = 90 \]
Now, we can find the Selling Price:
\[ SP = 360 + 90 = 450 \]

### Step 2: Understand the Relationship Between Marked Price (MP), Selling Price (SP), and Discount
The shopkeeper offers a discount of 10% on the marked price (MP). This means that the Selling Price (SP) is 90% of the Marked Price (MP):
\[ SP = MP - \text{Discount} \]
Since the discount is 10% of MP, we can express this as:
\[ SP = MP - 0.10 \times MP = 0.90 \times MP \]

### Step 3: Set Up the Equation
Now we can set up the equation using the Selling Price we calculated:
\[ 450 = 0.90 \times MP \]

### Step 4: Solve for Marked Price (MP)
To find MP, we can rearrange the equation:
\[ MP = \frac{450}{0.90} \]
Calculating this gives:
\[ MP = 500 \]

### Conclusion
The marked price of the article is Rs 500.

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