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The problem is asking to find the cost price of an item given a profit and a loss scenario:

- If the item is sold for Rs 2540, there is a profit.
- If the item is sold for Rs 1850, there is a loss.
- The profit amount when sold for Rs 2540 is the same as the loss amount when sold for Rs 1850.

Let the cost price of the item be \( x \).

### Solution
1. Since the profit when selling at Rs 2540 is equal to the loss when selling at Rs 1850, we can write:
   \[
   2540 - x = x - 1850
   \]

2. Simplifying the equation:
   \[
   2540 + 1850 = 2x
   \]
   \[
   4390 = 2x
   \]
   \[
   x = \frac{4390}{2}
   \]
   \[
   x = 2195
   \]

### Answer
The cost price of the item is **Rs 2195**, so the correct answer is:
**(B) Rs 2195**

Would you like further details on the solution or have any questions?

### Related Questions
1. What is the formula for calculating profit or loss given cost and selling prices?
2. How would you calculate the cost price if only the percentage of profit/loss is given?
3. How can you determine the selling price required to achieve a certain profit percentage?
4. What happens if the profit and loss amounts are different? How would the equation change?
5. How can you calculate the breakeven point in terms of cost and selling price?

#### Tip
In profit and loss problems, setting up equations based on equal profit or loss values can simplify finding unknown costs.

If an item is sold at Rs 2540, there is a profit, and if sold at Rs 1850, there is a loss. The profit amount is equal to the loss amount. Find the cost price of the item.

Solve a profit and loss problem where selling at Rs 2540 gives a profit and selling at Rs 1850 results in a loss. The profit equals the loss, helping determine the cost price. Suitable for Grades 9-10.

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