A shopkeeper sold an article for Rs 6750 after giving a discount of 10% on the labelled price. He would have carned a profit of 50%, had there been no discount. What was the actual percentage of profi carned?

Options

A. 36
B. 40
C. 44
D. 35

Answer

To solve the problem step by step, we will find the labeled price, the cost price, and then calculate the actual percentage of profit earned by the shopkeeper.

### Step 1: Determine the Selling Price after Discount
The selling price (SP) after a discount of 10% is given as Rs 6750.

### Step 2: Calculate the Labeled Price (LP)
Since a discount of 10% is given, the selling price is 90% of the labeled price. We can express this as:
\[ SP = LP \times \left(1 - \frac{10}{100}\right) \]
\[ 6750 = LP \times \frac{90}{100} \]
\[ 6750 = LP \times 0.9 \]
To find the labeled price (LP), we rearrange the equation:
\[ LP = \frac{6750}{0.9} \]
\[ LP = 7500 \]

### Step 3: Determine the Cost Price (CP)
We know that if there was no discount, the shopkeeper would have made a profit of 50%. This means:
\[ SP = CP \times \left(1 + \frac{50}{100}\right) \]
\[ 7500 = CP \times 1.5 \]
To find the cost price (CP), we rearrange the equation:
\[ CP = \frac{7500}{1.5} \]
\[ CP = 5000 \]

### Step 4: Calculate the Actual Profit Earned
Now, we can find the actual profit earned by the shopkeeper:
\[ \text{Profit} = SP - CP \]
\[ \text{Profit} = 6750 - 5000 \]
\[ \text{Profit} = 1750 \]

### Step 5: Calculate the Actual Percentage of Profit
To find the actual percentage of profit, we use the formula:
\[ \text{Percentage of Profit} = \left(\frac{\text{Profit}}{CP}\right) \times 100 \]
\[ \text{Percentage of Profit} = \left(\frac{1750}{5000}\right) \times 100 \]
\[ \text{Percentage of Profit} = 35\% \]

### Final Answer
The actual percentage of profit earned by the shopkeeper is **35%**.

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