The profit percent gained if an object is sold at Rs 464 is equals to the loss percent when the object is sold at Rs 436. Find the cost price of this object?

Options

A. 250
B. 400
C. 450
D. 500

Answer

To find the cost price of the object, we can follow these steps:

### Step 1: Define the Variables
Let the cost price of the object be \( X \).

### Step 2: Identify Selling Prices
We are given:
- Selling Price (SP) when profit is made: \( SP_1 = 464 \)
- Selling Price (SP) when loss is incurred: \( SP_2 = 436 \)

### Step 3: Set Up the Profit and Loss Percentages
According to the problem, the profit percentage when sold at Rs. 464 is equal to the loss percentage when sold at Rs. 436.

- Profit Percentage when sold at Rs. 464:
\[ \text{Profit \%} = \frac{SP_1 - CP}{CP} \times 100 = \frac{464 - X}{X} \times 100 \]

- Loss Percentage when sold at Rs. 436:
\[ \text{Loss \%} = \frac{CP - SP_2}{CP} \times 100 = \frac{X - 436}{X} \times 100 \]

### Step 4: Set the Profit Percentage Equal to the Loss Percentage
Since the profit percentage is equal to the loss percentage, we can set the two equations equal to each other:
\[ \frac{464 - X}{X} \times 100 = \frac{X - 436}{X} \times 100 \]

### Step 5: Simplify the Equation
We can cancel out the 100 from both sides:
\[ \frac{464 - X}{X} = \frac{X - 436}{X} \]

Now, cross-multiply:
\[ (464 - X) \cdot X = (X - 436) \cdot X \]

### Step 6: Expand and Rearrange
Expanding both sides gives:
\[ 464X - X^2 = X^2 - 436X \]

Now, rearranging the equation:
\[ 464X + 436X = 2X^2 \]
\[ 900X = 2X^2 \]

### Step 7: Divide by X (assuming \( X \neq 0 \))
We can simplify:
\[ 900 = 2X \]

### Step 8: Solve for X
Dividing both sides by 2:
\[ X = 450 \]

### Conclusion
The cost price of the object is Rs. 450.

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