A trader has a faulty balance that weighs `20%` less than what is should weigh. If he wants to earn `25%` profit, while offering a whopping `50%` discount by how much per cent should he mark up his goods?

Options

A. 80
B. 90
C. 100
D. 120

Answer

To solve the problem step by step, we need to analyze the situation involving the trader's faulty balance, profit margin, discount, and the required markup percentage.

### Step-by-Step Solution:

1. **Understanding the Faulty Balance**:
- The trader's balance weighs 20% less than it should. This means if he is supposed to sell 100 grams, he actually sells only 80 grams.
- Therefore, if the cost price (CP) of 100 grams is assumed to be `100` rupees, the cost price of 80 grams is `80` rupees.

**Hint**: Remember that a 20% reduction means the actual weight is 80% of the intended weight.

2. **Calculating Selling Price for Profit**:
- The trader wants to earn a profit of 25%.
- The profit percentage is calculated based on the cost price. If the CP is `80` rupees, then the selling price (SP) can be calculated using the formula:
\[ SP = CP + (Profit \% \times CP) = 80 + (25\% \times 80) = 80 + 20 = 100 \text{ rupees} \]

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

3. **Understanding the Discount**:
- The trader offers a discount of 50% on the marked price (MP).
- If the SP is `100` rupees after the discount, then the relationship between the SP and MP can be expressed as:
\[ SP = MP - (Discount \times MP) \Rightarrow 100 = MP - (50\% \times MP) \]
- This simplifies to:
\[ 100 = MP \times (1 - 0.5) = 0.5 \times MP \Rightarrow MP = \frac{100}{0.5} = 200 \text{ rupees} \]

**Hint**: A 50% discount means the selling price is half of the marked price.

4. **Calculating the Markup Percentage**:
- Now, we need to find out by how much percentage the trader marked up the price from the cost price to the marked price.
- The cost price for 100 grams is `100` rupees, and the marked price is `200` rupees.
- The markup can be calculated as:
\[ \text{Markup} = MP - CP = 200 - 100 = 100 \text{ rupees} \]
- The markup percentage is then calculated as:
\[ \text{Markup Percentage} = \left( \frac{Markup}{CP} \times 100 \right) = \left( \frac{100}{100} \times 100 \right) = 100\% \]

**Hint**: Markup percentage is calculated based on the cost price, so always use the cost price in your calculations.

### Final Answer:
The trader should mark up his goods by **100%**.