A shopkeeper purchases a product for Rs.100 and sells it making a profit of 10%. The customer resells it to the same shopkeeper incurring a loss of 10%. In these dealings the shopkeeper makes
Shopkeeper's Initial Sale Calculation
The shopkeeper purchases a product for Rs. 100.
- Cost Price (CP) = Rs. 100
- Profit percentage = 10%
- Profit amount = $10\% \text{ of } 100 = \frac{10}{100} \times 100 = \text{Rs. } 10$
- Selling Price (SP1) = CP + Profit amount = $100 + 10 = \text{Rs. } 110$
The shopkeeper initially sells the product for Rs. 110.
Customer's Resale Price Calculation
The customer buys the product for Rs. 110 and then resells it to the shopkeeper at a loss of 10%.
- Customer's purchase price = Rs. 110
- Loss percentage = 10%
- Loss amount = $10\% \text{ of } 110 = \frac{10}{100} \times 110 = \text{Rs. } 11$
- Resale Price (SP2) = Customer's purchase price - Loss amount = $110 - 11 = \text{Rs. } 99$
The customer resells the product to the shopkeeper for Rs. 99.
Shopkeeper's Net Profit Calculation
To find the shopkeeper's net profit in these dealings, consider the difference between the price they sold the item for initially and the price they bought it back for. This calculation assumes the shopkeeper ends up with the item.
- Initial Selling Price (SP1) = Rs. 110
- Buy-back Price (SP2) = Rs. 99
- Net Profit = SP1 - SP2 = $110 - 99 = \text{Rs. } 11$
Alternatively, compare the shopkeeper's final financial position to their initial one:
- Initial State: Rs. 100 cash, no product.
- Action 1: Buy product for Rs. 100. State: Rs. 0 cash, product.
- Action 2: Sell product for Rs. 110. State: Rs. 110 cash, no product.
- Action 3: Buy product back for Rs. 99. State: Rs. $110 - 99 = 11$ cash, product.
- Final State: Rs. 11 cash and the product.
- Compared to the initial state (Rs. 100 cash, no product), the shopkeeper has Rs. 11 cash and the product. This shows a net gain of Rs. 11 relative to the scenario where the shopkeeper simply kept the initial Rs. 100 cash.
Therefore, the shopkeeper makes a net profit of Rs. 11.
Important Questions from Profit & Loss (Notes)
- A person incurs a loss of 10% by selling a watch for Rs. 450. At what price should the watch be sold to earn 10% profit?
Two bikes were sold for a total of ₹ $1,50,000$. One bike was sold at $33\frac{1}{3}\%$ loss and the other at $20\%$ profit. The cost price of the first bike is equal to the selling price of the other bike. Find the over all loss.
What will be the profit percentage on selling an article at a certain price if there is $30\%$ loss on selling the article at $\frac{3}{5}$ of the selling price?
- 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?
