A wholesale dealer sold his goods to a retail dealer at a profit of 12 `1/2` %. The retail dealer gained 20% by selling the goods for 3240. The cost price of the whole sale dealer was

Options

A. 2625
B. 2575
C. 2500
D. 2400

Answer

To find the cost price of the wholesale dealer, we will follow these steps:

### Step 1: Understand the Selling Price of the Retail Dealer
The retail dealer sold the goods for ₹3240 at a profit of 20%.

### Step 2: Calculate the Cost Price of the Retail Dealer
Let the cost price of the retail dealer be \( CP_{retail} \). Since the selling price (SP) is given as ₹3240 and the profit is 20%, we can use the formula:

\[ SP = CP_{retail} + \text{Profit} \]

The profit can be expressed as:

\[ \text{Profit} = 20\% \text{ of } CP_{retail} = \frac{20}{100} \times CP_{retail} = \frac{1}{5} \times CP_{retail} \]

Thus, we can write:

\[ 3240 = CP_{retail} + \frac{1}{5} \times CP_{retail} \]

Combining the terms gives:

\[ 3240 = \frac{6}{5} \times CP_{retail} \]

### Step 3: Solve for \( CP_{retail} \)
To find \( CP_{retail} \), we rearrange the equation:

\[ CP_{retail} = 3240 \times \frac{5}{6} \]

Calculating this gives:

\[ CP_{retail} = 2700 \]

### Step 4: Calculate the Selling Price of the Wholesale Dealer
The wholesale dealer sold the goods at a profit of 12.5%. Let the cost price of the wholesale dealer be \( CP_{wholesale} \). The selling price of the wholesale dealer can be expressed as:

\[ SP_{wholesale} = CP_{wholesale} + \text{Profit} \]

The profit is:

\[ \text{Profit} = 12.5\% \text{ of } CP_{wholesale} = \frac{12.5}{100} \times CP_{wholesale} = \frac{1}{8} \times CP_{wholesale} \]

Thus, we can write:

\[ SP_{wholesale} = CP_{wholesale} + \frac{1}{8} \times CP_{wholesale} = \frac{9}{8} \times CP_{wholesale} \]

### Step 5: Set the Selling Price of the Wholesale Dealer Equal to the Cost Price of the Retail Dealer
Since the selling price of the wholesale dealer is equal to the cost price of the retail dealer:

\[ \frac{9}{8} \times CP_{wholesale} = 2700 \]

### Step 6: Solve for \( CP_{wholesale} \)
Rearranging gives:

\[ CP_{wholesale} = 2700 \times \frac{8}{9} \]

Calculating this gives:

\[ CP_{wholesale} = 2400 \]

### Final Answer
The cost price of the wholesale dealer is ₹2400.

---