A shopkeeper announced a 30% discount on the marked price of an item. A person bought the item from the shop for Rs 21,000 after getting the discount, and sold the item to a customer in such a way that he earned a profit of 32% on the marked price. What is the profit (in Rs) the person eamed by selling the item?

Options

A. 9600
B. 21600
C. 18600
D. 10000

Answer

To solve the problem step by step, we need to find the profit earned by the person who bought an item after a discount and then sold it for a profit based on the marked price.

### Step 1: Determine the Marked Price (MP)
Let the marked price of the item be \( MP \).

The shopkeeper announced a 30% discount on the marked price. Therefore, the selling price (SP) after the discount can be calculated as:
\[ SP = MP - (30\% \text{ of } MP) = MP - 0.3 \times MP = 0.7 \times MP \]

### Step 2: Calculate the Marked Price using the Selling Price
According to the problem, the person bought the item for Rs 21,000 after the discount:
\[ 0.7 \times MP = 21000 \]
To find the marked price, we can rearrange the equation:
\[ MP = \frac{21000}{0.7} = 30000 \]

### Step 3: Calculate the Selling Price for a 32% Profit
The person wants to earn a profit of 32% on the marked price. The profit can be calculated as:
\[ \text{Profit} = 32\% \text{ of } MP = 0.32 \times MP = 0.32 \times 30000 = 9600 \]
Now, the selling price (SP) when he sells the item can be calculated as:
\[ SP = MP + \text{Profit} = 30000 + 9600 = 39600 \]

### Step 4: Calculate the Profit Earned by Selling the Item
The profit earned by the person when he sells the item can be calculated as:
\[ \text{Profit Earned} = SP - \text{Cost Price (CP)} = 39600 - 21000 = 18600 \]

### Final Answer
The profit earned by the person by selling the item is Rs 18600.

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