Mohan sold an item for ₹4,510 and incurred a loss of 45%. At what price should he have sold the item to have gained a profit of 45%?

Options

A. ₹10,900
B. ₹12,620
C. ₹11,890
D. Cannot be determined

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the loss percentage
Mohan incurred a loss of 45%. This means that if we consider the cost price (CP) of the item as 100 units, the selling price (SP) will be 55 units (since 100 - 45 = 55).

**Hint:** Remember that a loss of 45% means you are left with 55% of the cost price.

### Step 2: Calculate the selling price in terms of cost price
Given that Mohan sold the item for ₹4,510, we can set up the equation:
- 55 units = ₹4,510

**Hint:** This allows us to find the value of one unit.

### Step 3: Calculate the value of one unit
To find the value of one unit, we divide the selling price by the number of units:
- Value of one unit = ₹4,510 / 55 = ₹82

**Hint:** Make sure to perform the division carefully to avoid mistakes.

### Step 4: Calculate the cost price
Since we established that 100 units represent the cost price, we can calculate the cost price:
- Cost Price (CP) = 100 units × ₹82 = ₹8,200

**Hint:** The cost price is always higher than the selling price when there is a loss.

### Step 5: Calculate the desired selling price for a profit of 45%
To find out at what price Mohan should have sold the item to gain a profit of 45%, we first need to calculate 45% of the cost price:
- Profit = 45% of ₹8,200 = 0.45 × ₹8,200 = ₹3,690

**Hint:** Remember that profit is calculated based on the cost price.

### Step 6: Calculate the new selling price
Now, we add the profit to the cost price to find the new selling price:
- New Selling Price = Cost Price + Profit = ₹8,200 + ₹3,690 = ₹11,890

**Hint:** This final step combines the cost price and the profit to get the selling price.

### Final Answer
Mohan should have sold the item for ₹11,890 to gain a profit of 45%.