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.
Important Questions from Profit & Loss (Notes)
- A shopkeeper bought an item for ₹7825 and marked it at 30% higher than the cost price. If he sells the item by allowing 20% discount, then his profit percentage will be :
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?
- A shopkeeper earned a profit (in ₹) by selling an item, which is three times the discount offered (in ₹). If the discount offered is 6.25%, what is his profit percentage ?
- The Loss incurred by selling an article at Rs.$2042$ is $75\%$ of the gain attained by selling the same article at Rs.$2532$. Find the cost price of the article. (In Rs.)
