This question asks us to find the selling price of a watch that ensures a 10% profit, given the initial selling price was Rs. 450 resulting in a 10% loss.

Calculating Cost Price from Loss

First, we need to determine the original cost price (CP) of the watch. We know that selling the watch for Rs. 450 resulted in a 10% loss.

The formula relating Selling Price (SP), Cost Price (CP), and Loss Percentage (Loss%) is:

SP = CP * (100 - Loss%) / 100

We are given:

• SP = Rs. 450
• Loss% = 10%

Plugging these values into the formula:

Rs. 450 = CP * (100 - 10) / 100

Rs. 450 = CP * (90 / 100)

To find the CP, we rearrange the formula:

CP = Rs. 450 * (100 / 90)

CP = Rs. 450 * (10 / 9)

CP = Rs. 50 * 10

CP = Rs. 500

So, the cost price of the watch is Rs. 500.

Calculating Selling Price for Profit

Next, we need to find the selling price (let's call it SP') that would yield a 10% profit. We will use the cost price we just calculated (Rs. 500).

The formula relating Selling Price (SP), Cost Price (CP), and Profit Percentage (Profit%) is:

SP' = CP * (100 + Profit%) / 100

We have:

• CP = Rs. 500
• Profit% = 10%

Plugging these values into the formula:

SP' = Rs. 500 * (100 + 10) / 100

SP' = Rs. 500 * (110 / 100)

SP' = Rs. 500 * (11 / 10)

SP' = Rs. 50 * 11

SP' = Rs. 550

Therefore, the watch should be sold for Rs. 550 to earn a 10% profit.