A merchant marks the price of his articles 20% above the cost price. If he allows 20% discount, what is the profit or loss per cent ?

Options

A. 2% loss
B. 4% profit
C. 4% loss
D. No profit/loss

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Cost Price (CP)
Let's assume the Cost Price (CP) of the article is ₹100.

**Hint:** Start by assuming a simple value for CP to make calculations easier.

### Step 2: Calculate the Marked Price (MP)
The merchant marks the price 20% above the Cost Price. Therefore, we can calculate the Marked Price (MP) as follows:

\[ MP = CP + (20\% \text{ of } CP) = 100 + (0.20 \times 100) = 100 + 20 = ₹120 \]

**Hint:** Remember that "20% above" means you add 20% of the CP to the original CP.

### Step 3: Calculate the Selling Price (SP)
The merchant allows a 20% discount on the Marked Price. To find the Selling Price (SP), we can calculate it as follows:

\[ SP = MP - (20\% \text{ of } MP) = 120 - (0.20 \times 120) = 120 - 24 = ₹96 \]

**Hint:** A discount means you subtract the percentage from the marked price.

### Step 4: Determine Profit or Loss
Now we need to compare the Selling Price (SP) with the Cost Price (CP) to determine if there is a profit or loss.

Since SP (₹96) is less than CP (₹100), there is a loss.

**Hint:** If SP is less than CP, it indicates a loss.

### Step 5: Calculate the Loss Amount
The loss amount can be calculated as:

\[ \text{Loss} = CP - SP = 100 - 96 = ₹4 \]

**Hint:** The loss amount is simply the difference between CP and SP.

### Step 6: Calculate the Loss Percentage
Finally, we can calculate the loss percentage using the formula:

\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100 = \left(\frac{4}{100}\right) \times 100 = 4\% \]

**Hint:** The loss percentage is calculated based on the cost price.

### Conclusion
The merchant incurs a loss of 4%.

**Final Answer:** 4% loss.

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