The balance of a trader weight 10% less than it should be still the trader marks up his goods to get the overall profit of 20% . What is the markup on the cost price.

Answer

To solve the problem step by step, we will analyze the situation involving the trader, the weight of the goods, and the profit margin.

### Step 1: Understand the Weight Discrepancy
The trader's balance weighs 10% less than it should. This means that if the actual weight of the goods is supposed to be 10 units, the trader's balance shows only 9 units.

**Hint:** Remember that a 10% reduction in weight means the trader is giving less product than he claims.

### Step 2: Determine the Cost Price
Assuming the cost price of 1 unit (or 1 gram) is 1 rupee, the cost price for 10 units would be:
\[ \text{Cost Price (CP)} = 10 \text{ units} \times 1 \text{ rupee/unit} = 10 \text{ rupees} \]

**Hint:** Always start by determining the cost price based on the actual weight of the goods.

### Step 3: Calculate the Selling Price for a 20% Profit
To achieve a 20% profit on the cost price, the selling price (SP) must be:
\[ \text{Selling Price (SP)} = \text{Cost Price} + 20\% \text{ of Cost Price} \]
\[ SP = 10 + 0.2 \times 10 = 10 + 2 = 12 \text{ rupees} \]

**Hint:** Profit is calculated as a percentage of the cost price, so be sure to add it to the cost price to find the selling price.

### Step 4: Calculate the Actual Selling Price per Measured Unit
Since the trader sells 9 units (due to the weight discrepancy), he sells these 9 units for 12 rupees. Therefore, the selling price per measured unit is:
\[ \text{Selling Price per unit} = \frac{12 \text{ rupees}}{9 \text{ units}} = \frac{4}{3} \text{ rupees/unit} \approx 1.33 \text{ rupees/unit} \]

**Hint:** When calculating selling price per unit, divide the total selling price by the number of units sold.

### Step 5: Determine the Markup on the Cost Price
The markup is the difference between the selling price per unit and the cost price per unit. The cost price per unit is 1 rupee, so the markup is:
\[ \text{Markup} = \text{Selling Price per unit} - \text{Cost Price per unit} \]
\[ \text{Markup} = \frac{4}{3} - 1 = \frac{4}{3} - \frac{3}{3} = \frac{1}{3} \text{ rupee} \]

**Hint:** Markup is calculated by subtracting the cost price from the selling price.

### Step 6: Calculate the Markup Percentage
To find the markup percentage based on the cost price:
\[ \text{Markup Percentage} = \left(\frac{\text{Markup}}{\text{Cost Price per unit}}\right) \times 100 \]
\[ \text{Markup Percentage} = \left(\frac{\frac{1}{3}}{1}\right) \times 100 = \frac{1}{3} \times 100 \approx 33.33\% \]

**Hint:** Markup percentage is expressed as a percentage of the cost price, so always divide the markup by the cost price before multiplying by 100.

### Final Answer
The markup on the cost price is approximately **33.33%**.