A trader has a faulty balance that weighs `20%` less than what it should weigh. What should be the minimum mark up per cent, if he wants to earn `50%` profit?

Options

A. 12.5
B. 16.67
C. 20
D. 25

Answer

To solve the problem step by step, we need to determine the minimum markup percentage the trader should apply to achieve a 50% profit while using a faulty balance that weighs 20% less.

### Step-by-Step Solution:

1. **Assume the Cost Price (CP)**:
Let's assume the cost price of 1 gram of the product is ₹1. Therefore, the cost price for 100 grams will be:
\[ \text{CP for 100 grams} = 100 \times 1 = ₹100 \]

**Hint**: Start by defining the cost price for a standard quantity to simplify calculations.

2. **Calculate the Actual Weight Sold**:
Since the trader's balance weighs 20% less, when he claims to sell 100 grams, he is actually selling:
\[ \text{Actual weight sold} = 100 \text{ grams} - (20\% \text{ of } 100 \text{ grams}) = 100 - 20 = 80 \text{ grams} \]

**Hint**: Remember that a 20% reduction means the trader is only giving 80% of the claimed weight.

3. **Determine the Cost Price for the Actual Weight Sold**:
The cost price for the 80 grams he actually sells is:
\[ \text{CP for 80 grams} = 80 \times 1 = ₹80 \]

**Hint**: Calculate the cost price based on the actual quantity being sold.

4. **Calculate the Selling Price (SP) for 50% Profit**:
To achieve a 50% profit, the selling price must be:
\[ \text{SP} = \text{CP} + \text{Profit} = \text{CP} + 50\% \text{ of CP} \]
\[ \text{SP} = 80 + 0.5 \times 80 = 80 + 40 = ₹120 \]

**Hint**: Profit can be calculated as a percentage of the cost price.

5. **Determine the Marked Price (MP)**:
The trader needs to set a marked price that allows him to sell the 80 grams for ₹120. Since he is selling 80 grams but claims to sell 100 grams, we need to find the marked price for 100 grams:
\[ \text{MP for 100 grams} = \text{SP for 80 grams} = ₹120 \]

**Hint**: The marked price should reflect the selling price for the actual quantity sold.

6. **Calculate the Required Markup Percentage**:
The markup percentage is calculated based on the cost price for 100 grams:
\[ \text{Markup} = \frac{\text{MP} - \text{CP}}{\text{CP}} \times 100 \]
\[ \text{Markup} = \frac{120 - 100}{100} \times 100 = \frac{20}{100} \times 100 = 20\% \]

**Hint**: Markup percentage measures how much more than the cost price the selling price is.

### Final Answer:
The minimum markup percentage the trader should apply is **20%**.