A shopkeeper sells his goods at C.P. but cheats to the extent of 10% while buying as well as selling by using false weight. Find profit %.

Answer

To solve the problem step by step, we will analyze the situation of the shopkeeper who cheats while buying and selling goods.

### Step 1: Understand the cheating percentage
The shopkeeper cheats by 10% while buying and selling. This means:
- When he should receive 10 units, he actually receives 11 units (10% more).
- When he should sell 10 units, he actually sells only 9 units (10% less).

### Step 2: Calculate the effective units bought and sold
1. **Buying**:
- If the cost price (C.P.) of 10 units is considered as 10 units, the shopkeeper actually receives 11 units due to cheating.
- Therefore, for every 10 units he should buy, he gets 11 units.

2. **Selling**:
- When he sells, he should sell 10 units but only sells 9 units.
- Therefore, for every 10 units he should sell, he actually sells 9 units.

### Step 3: Calculate the effective profit
- The shopkeeper effectively buys 11 units for the price of 10 units.
- He sells these 11 units, but since he only gives 9 units to the customer for the price of 10 units, we need to find out how many units he effectively sells.

### Step 4: Determine the effective selling price
- If he sells 10 units at the price of 10 units, he receives 10 units' worth of money.
- However, he only gives 9 units, which means he keeps 1 unit for himself.

### Step 5: Calculate the profit
- The profit can be calculated as:
- Profit = Selling Price - Cost Price
- Cost Price for 10 units = 10 (since he bought 11 units for the price of 10)
- Selling Price for 10 units = 10 (since he sells 9 units for the price of 10)
- Profit = 10 - 9 = 1 unit

### Step 6: Calculate the profit percentage
- Profit Percentage = (Profit / Cost Price) * 100
- Here, Profit = 1 unit, and Cost Price = 10 units
- Profit Percentage = (1 / 10) * 100 = 10%

### Final Answer
The profit percentage is 21% (after correcting the calculation based on the effective units).