A man buys an article for Rs 80 and marks it at Rs 120, He then allows a discount of 40%. What is the loss or gain%?

Options

A. 12% gain
B. 12% loss
C. 10% gain
D. 10% loss

Answer

To find the loss or gain percentage, we can follow these steps:

### Step 1: Determine the Cost Price (CP)
The cost price of the article is given as:
\[ \text{Cost Price (CP)} = Rs. 80 \]

### Step 2: Determine the Marked Price (MP)
The marked price of the article is given as:
\[ \text{Marked Price (MP)} = Rs. 120 \]

### Step 3: Calculate the Discount
The discount allowed on the marked price is 40%. To find the discount amount, we can use the formula:
\[ \text{Discount} = \text{Marked Price} \times \frac{\text{Discount Percentage}}{100} \]
Substituting the values:
\[ \text{Discount} = 120 \times \frac{40}{100} = 120 \times 0.4 = Rs. 48 \]

### Step 4: Calculate the Selling Price (SP)
The selling price can be calculated by subtracting the discount from the marked price:
\[ \text{Selling Price (SP)} = \text{Marked Price} - \text{Discount} \]
Substituting the values:
\[ \text{Selling Price (SP)} = 120 - 48 = Rs. 72 \]

### Step 5: Calculate the Gain or Loss
To determine if there is a gain or loss, we compare the selling price with the cost price:
- If SP > CP, there is a gain.
- If SP < CP, there is a loss.

In this case:
\[ \text{Selling Price (SP)} = Rs. 72 \]
\[ \text{Cost Price (CP)} = Rs. 80 \]

Since \( SP < CP \), there is a loss.

### Step 6: Calculate the Loss Amount
The loss amount can be calculated as:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]
Substituting the values:
\[ \text{Loss} = 80 - 72 = Rs. 8 \]

### Step 7: Calculate the Loss Percentage
The loss percentage can be calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{8}{80} \right) \times 100 = 10\% \]

### Final Answer
The loss percentage is **10%**.

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