A man sells his goods at 20% profit Had he purchase it for Rs.600 less and sold it for Rs. 400 less then he would gain 10% more profit. Find the initial cost price.

Options

A. Rs 3900
B. Rs 3800
C. Rs 4200
D. Rs 4000

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Define the Initial Cost Price
Let the initial cost price (CP) be represented as \( 5X \).

**Hint:** Assign a variable to the initial cost price to simplify calculations.

### Step 2: Calculate the Selling Price with Initial Profit
Since the man sells his goods at a 20% profit, the selling price (SP) can be calculated as:
\[ SP = CP + 20\% \text{ of } CP = 5X + 0.2 \times 5X = 6X \]

**Hint:** Remember that selling price is calculated by adding the profit to the cost price.

### Step 3: Define the New Cost Price
If he had purchased the goods for Rs. 600 less, the new cost price (CP2) would be:
\[ CP2 = 5X - 600 \]

**Hint:** Adjust the cost price based on the given condition in the problem.

### Step 4: Define the New Selling Price
If he sold it for Rs. 400 less, the new selling price (SP2) would be:
\[ SP2 = 6X - 400 \]

**Hint:** Adjust the selling price according to the problem's conditions.

### Step 5: Define the New Profit Percentage
The problem states that with the new cost price and selling price, he would gain 10% more profit than the original 20%. Therefore, the new profit percentage is:
\[ 20\% + 10\% = 30\% \]

**Hint:** Understand how profit percentages can be increased based on the problem's conditions.

### Step 6: Set Up the Profit Ratio
The profit ratio for the new scenario can be expressed as:
\[ \text{Profit} = 30\% \text{ of } CP2 = 0.3 \times (5X - 600) \]
Thus, the selling price can also be expressed as:
\[ SP2 = CP2 + \text{Profit} = (5X - 600) + 0.3 \times (5X - 600) \]

**Hint:** Use the profit percentage to express the selling price in terms of the new cost price.

### Step 7: Set Up the Equation
From the previous steps, we can equate the two expressions for SP2:
\[ 6X - 400 = (5X - 600) + 0.3 \times (5X - 600) \]

### Step 8: Simplify the Equation
Expanding the right side:
\[ 6X - 400 = (5X - 600) + (1.5X - 180) \]
\[ 6X - 400 = 6.5X - 780 \]

### Step 9: Solve for X
Rearranging the equation:
\[ 6X - 6.5X = -780 + 400 \]
\[ -0.5X = -380 \]
\[ X = \frac{380}{0.5} = 760 \]

### Step 10: Calculate the Initial Cost Price
Now, substituting back to find the initial cost price:
\[ CP = 5X = 5 \times 760 = 3800 \]

**Final Answer:** The initial cost price is Rs. 3800.