A shopkeeper sold an article at a loss of 20%. But if he could sell it at Rs. 200 more, he could earn a profit of 5%. The cost price of the article is

Options

A. Rs.800
B. Rs.1000
C. Rs.1200
D. Rs.66

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Cost Price (CP)
Let the Cost Price (CP) of the article be Rs. 100 (we can use any value, but 100 makes calculations easier).

### Step 2: Calculate Selling Price at a Loss of 20%
A loss of 20% means that the selling price (SP) will be 80% of the cost price.
- Selling Price at a loss (SP1) = CP - (20% of CP)
- SP1 = 100 - (20/100 * 100) = 100 - 20 = Rs. 80

### Step 3: Calculate Selling Price at a Profit of 5%
A profit of 5% means that the selling price will be 105% of the cost price.
- Selling Price at a profit (SP2) = CP + (5% of CP)
- SP2 = 100 + (5/100 * 100) = 100 + 5 = Rs. 105

### Step 4: Establish the Relationship Between SP1 and SP2
According to the problem, if the shopkeeper sold the article for Rs. 200 more than the selling price at a loss, he would earn a profit of 5%. Therefore, we can set up the equation:
- SP2 = SP1 + 200
- 105 = 80 + 200

### Step 5: Solve for the Cost Price
From the equation established in Step 4, we can see that:
- SP2 - SP1 = 200
- 105 - 80 = 200
- 25 = 200 (This is incorrect based on our assumption of CP = 100)

### Step 6: Correct the Assumption
We need to find the actual CP. Let's denote the actual CP as 'x'.
- SP1 = x - 0.2x = 0.8x
- SP2 = x + 0.05x = 1.05x
- According to the problem: 1.05x = 0.8x + 200

### Step 7: Rearranging the Equation
Now, we will rearrange the equation:
- 1.05x - 0.8x = 200
- 0.25x = 200

### Step 8: Solve for x (Cost Price)
Now, we can solve for x:
- x = 200 / 0.25
- x = 800

### Final Answer
The Cost Price of the article is Rs. 800.

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