A shopkeeper calculates percentage profit on the buying price and another on the selling price. What will be their difference in profits if both claim a profit of 20% on goods sold for Rs. 3000?

Options

A. Rs. 200
B. Rs. 100
C. Rs. 400
D. Rs. 150

Answer

To solve the problem, we need to determine the difference in profits calculated by the shopkeeper based on the buying price and the selling price. Let's break it down step by step.

### Step 1: Determine the Selling Price
The selling price (SP) of the goods is given as Rs. 3000.

### Step 2: Calculate the Cost Price Based on Profit Percentage
Let the cost price (CP) be represented as \( 100x \).

Since the shopkeeper claims a profit of 20% on the cost price, we can calculate the selling price using the formula:
\[ SP = CP + \text{Profit} \]
Where:
\[ \text{Profit} = 20\% \text{ of } CP = 0.20 \times CP = 0.20 \times 100x = 20x \]
Thus, the selling price becomes:
\[ SP = 100x + 20x = 120x \]

### Step 3: Set the Selling Price Equal to Rs. 3000
Since we know the selling price is Rs. 3000, we can set up the equation:
\[ 120x = 3000 \]

### Step 4: Solve for x
To find the value of \( x \), we divide both sides by 120:
\[ x = \frac{3000}{120} = 25 \]

### Step 5: Calculate the Cost Price
Now that we have \( x \), we can find the cost price:
\[ CP = 100x = 100 \times 25 = 2500 \]

### Step 6: Calculate the Profit Based on Selling Price
Now, if the shopkeeper calculates profit based on the selling price, we need to find the cost price that would give a 20% profit on the selling price:
\[ \text{Profit} = 20\% \text{ of } SP = 0.20 \times 3000 = 600 \]
Thus, the cost price when calculating profit based on selling price would be:
\[ CP = SP - \text{Profit} = 3000 - 600 = 2400 \]

### Step 7: Calculate the Profit Based on Buying Price
Now, we can calculate the profit based on the buying price:
\[ \text{Profit based on CP} = SP - CP = 3000 - 2500 = 500 \]

### Step 8: Calculate the Profit Based on Selling Price
The profit based on the selling price we calculated earlier is:
\[ \text{Profit based on SP} = 600 \]

### Step 9: Find the Difference in Profits
Finally, we find the difference in profits calculated:
\[ \text{Difference} = \text{Profit based on SP} - \text{Profit based on CP} = 600 - 500 = 100 \]

### Final Answer
The difference in profits is Rs. 100.

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