Even after reducing the marked price of a Table by Rs.576, a shopkeeper makes a profit of 20%. If the cost price of table is Rs.3840, what % of profit would he have made if he had sold the Table at the marked price?

Options

A. `40%`
B. `35%`
C. `32%`
D. `36.36%`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the Cost Price
The cost price (CP) of the table is given as Rs. 3840.

### Step 2: Calculate the Selling Price with 20% Profit
To find the selling price (SP) when the shopkeeper makes a profit of 20%, we use the formula:
\[ SP = CP \times \left(1 + \frac{Profit\ Percentage}{100}\right) \]
Substituting the values:
\[ SP = 3840 \times \left(1 + \frac{20}{100}\right) \]
\[ SP = 3840 \times 1.2 \]
\[ SP = 4608 \]

### Step 3: Find the Marked Price
The marked price (MP) is the selling price plus the discount. The discount given is Rs. 576. Therefore:
\[ MP = SP + Discount \]
Substituting the values:
\[ MP = 4608 + 576 \]
\[ MP = 5184 \]

### Step 4: Calculate the Profit at Marked Price
Now, we need to find the profit if the table is sold at the marked price. The profit can be calculated as:
\[ Profit = MP - CP \]
Substituting the values:
\[ Profit = 5184 - 3840 \]
\[ Profit = 1344 \]

### Step 5: Calculate the Profit Percentage at Marked Price
To find the profit percentage, we use the formula:
\[ Profit\ Percentage = \left(\frac{Profit}{CP}\right) \times 100 \]
Substituting the values:
\[ Profit\ Percentage = \left(\frac{1344}{3840}\right) \times 100 \]
Calculating:
\[ Profit\ Percentage = 0.35 \times 100 \]
\[ Profit\ Percentage = 35\% \]

### Final Answer
The percentage of profit that the shopkeeper would have made if he had sold the table at the marked price is **35%**.

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