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?

Answer

To solve the problem step by step, we will follow the given information and apply the necessary calculations.

### Step 1: Identify the Marked Price
The marked price (MP) of the article is given as Rs 500.

### Step 2: Calculate the Discount
The discount offered by the shopkeeper is 10% of the marked price.
- Discount = 10% of Rs 500
- Discount = (10/100) * 500 = Rs 50

### Step 3: Calculate the Selling Price
The selling price (SP) can be calculated by subtracting the discount from the marked price.
- Selling Price = Marked Price - Discount
- Selling Price = Rs 500 - Rs 50 = Rs 450

### Step 4: Understand the Profit Percentage
The shopkeeper makes a profit of 20%. This means that the selling price is 120% of the cost price (CP).

### Step 5: Set Up the Equation for Cost Price
Using the relationship between selling price, cost price, and profit percentage:
- Selling Price = Cost Price + Profit
- Selling Price = Cost Price + (20% of Cost Price)
- Selling Price = Cost Price * (1 + 20/100)
- Selling Price = Cost Price * (1 + 0.2) = Cost Price * 1.2

### Step 6: Rearranging the Equation
We can rearrange the equation to find the cost price:
- Cost Price = Selling Price / 1.2

### Step 7: Substitute the Selling Price
Now substitute the selling price we calculated:
- Cost Price = Rs 450 / 1.2

### Step 8: Perform the Calculation
- Cost Price = Rs 450 / 1.2 = Rs 375

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

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