The marked price of an article is 60% more than its cost price. If the article is sold for Rs. 300 after offering a discount of Rs. 20, then what will be the profit per cent ?

Options

A. 40
B. 50
C. 25
D. 45

Answer

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

### Step 1: Understand the relationship between cost price (CP) and marked price (MP)
The marked price of the article is 60% more than its cost price. We can express this mathematically:
\[ \text{MP} = \text{CP} + 0.6 \times \text{CP} = 1.6 \times \text{CP} \]

### Step 2: Determine the selling price (SP) after discount
The article is sold for Rs. 300 after offering a discount of Rs. 20. Therefore, we can find the marked price:
\[ \text{SP} = \text{MP} - \text{Discount} \]
\[ 300 = \text{MP} - 20 \]
\[ \text{MP} = 300 + 20 = 320 \]

### Step 3: Set up the equation for cost price using the marked price
From Step 1, we know:
\[ \text{MP} = 1.6 \times \text{CP} \]
Substituting the value of MP we found:
\[ 320 = 1.6 \times \text{CP} \]

### Step 4: Solve for the cost price (CP)
To find the cost price, rearrange the equation:
\[ \text{CP} = \frac{320}{1.6} \]
Calculating this gives:
\[ \text{CP} = 200 \]

### Step 5: Calculate the profit
The profit can be calculated as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values we have:
\[ \text{Profit} = 300 - 200 = 100 \]

### Step 6: Calculate the profit percentage
Profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{100}{200} \right) \times 100 = 50\% \]

### Final Answer:
The profit percentage is **50%**.

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