The percentage profit earned by James when selling an item for ₹ 1,920 is equal to the percentage loss he incurs when selling the same item for ₹ 1,500. If he wants to earn a 10% profit, at what selling price should he sell the item?

Correct option is C

Given:

Selling price when there is a percentage profit = ₹ 1,920
Selling price when there is a percentage loss = ₹ 1,500
Required profit percentage = 10%

Formula Used: 

Let the cost price (CP) be x .
Since the percentage profit on selling at ₹ 1,920 is equal to the percentage loss on selling at ₹ 1,500:
$$Profit or Loss Percentage = \frac{|\text{SP} - \text{CP}|}{\text{CP}} \times 100$$

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To find the new selling price for a 10% profit: New SP

$$= \text{CP} \times \left(1 + \frac{10}{100}\right)$$

Solution:

1. Set up the equation based on the given condition:

- Profit percentage when SP = 1,920 is equal to loss percentage when SP = 1,500

​$$- \frac{1920 - x}{x} \times 100 = \frac{x - 1500}{x} \times 100$$ 

2. Solve for x :

1920 - x = x - 1500

1920 + 1500 = 2x

​$$x = \frac{3420}{2} = 1710$$​

So, the cost price (CP) = 1710

3. Calculate the selling price for a 10% profit:

New SP $$= 1710 \times \left(1 + \frac{10}{100}\right)$$​

New SP $$= 1710 \times 1.1 = 1881$$ 

Answer: To earn a 10% profit, James should sell the item at ₹ 1,881.