A shopkeeper offers 10% discount on the marked price of his articles and still makes a profit of 20%. What is the actual cost of the article marked Rs. 500 for him ?

Options

A. Rs. 440
B. Rs. 425
C. Rs. 400
D. Rs. 375

Answer

To find the actual cost of the article marked at Rs. 500, we can follow these steps:

### Step 1: Understand the relationship between Cost Price (CP), Marked Price (MP), and Selling Price (SP)
The shopkeeper offers a 10% discount on the marked price and still makes a profit of 20%. We can express these relationships mathematically.

### Step 2: Calculate the Selling Price (SP)
The Selling Price (SP) after a 10% discount on the Marked Price (MP) can be calculated as follows:
- Marked Price (MP) = Rs. 500
- Discount = 10% of MP = 10% of 500 = 0.10 * 500 = Rs. 50
- Therefore, Selling Price (SP) = MP - Discount = 500 - 50 = Rs. 450

### Step 3: Relate Selling Price to Cost Price
Since the shopkeeper makes a profit of 20%, we can express the Selling Price in terms of Cost Price (CP):
- Profit = 20% of CP
- Therefore, SP = CP + Profit = CP + 0.20 * CP = 1.20 * CP

### Step 4: Set up the equation
Now we can set the Selling Price equal to the expression we found:
\[ 450 = 1.20 \times CP \]

### Step 5: Solve for Cost Price (CP)
To find CP, we can rearrange the equation:
\[ CP = \frac{450}{1.20} \]
Calculating this gives:
\[ CP = 375 \]

### Conclusion
The actual cost of the article for the shopkeeper is Rs. 375.

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