Profit after selling a commodity for 524 is the same as loss after selling it for 452. The cost price of the commodity is

Options

A. 480
B. 500
C. 488
D. 485

Answer

To find the cost price (CP) of the commodity based on the information given in the question, we can follow these steps:

### Step 1: Understand the given information
We know that:
- Selling Price (SP) when there is a profit = 524
- Selling Price (SP) when there is a loss = 452
- Profit when selling at 524 is equal to the loss when selling at 452.

### Step 2: Write the formulas for profit and loss
- Profit = Selling Price - Cost Price
- Loss = Cost Price - Selling Price

### Step 3: Set up the equations
From the information given:
1. Profit when selling at 524:
\[ \text{Profit} = 524 - \text{CP} \]
2. Loss when selling at 452:
\[ \text{Loss} = \text{CP} - 452 \]

Since the profit is equal to the loss, we can set the two equations equal to each other:
\[ 524 - \text{CP} = \text{CP} - 452 \]

### Step 4: Solve for CP
Now, we will solve the equation:
1. Rearranging gives us:
\[ 524 + 452 = 2\text{CP} \]
\[ 976 = 2\text{CP} \]
2. Now, divide both sides by 2:
\[ \text{CP} = \frac{976}{2} = 488 \]

### Conclusion
The cost price of the commodity is **488**.

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