A retailer uses faulty balances to purchase and sell the goods. He uses his faulty balances in such a way that while buying the goods from wholesaler he gets `20%` more of what he pays for, while selling his goods to his customer he gives `10%` less of what he charges for. If he earns a profit of `60%` by how much per cent does he mark up his goods?

Options

A. 40
B. 44.44
C. 20
D. 56.67

Answer

To solve the problem step by step, we will analyze the retailer's buying and selling process, calculate the effective cost price, selling price, and the markup percentage.

### Step-by-Step Solution:

1. **Understanding the Buying Process:**
- When the retailer pays for 100 grams of goods, he actually receives 20% more due to the faulty balance.
- Therefore, if he pays for 100 grams, he actually receives:
\[ \text{Received Quantity} = 100 \text{ grams} + 20\% \text{ of } 100 \text{ grams} = 100 + 20 = 120 \text{ grams} \]

2. **Cost Price Calculation:**
- Let’s assume the cost price for 100 grams is `100` rupees.
- Thus, the cost price per gram is:
\[ \text{Cost Price per gram} = \frac{100 \text{ rupees}}{100 \text{ grams}} = 1 \text{ rupee/gram} \]
- The total cost for the 120 grams he actually receives is still `100` rupees.

3. **Understanding the Selling Process:**
- When selling, the retailer charges for 100 grams but gives 10% less.
- Therefore, when he charges for 100 grams, he actually sells:
\[ \text{Sold Quantity} = 100 \text{ grams} - 10\% \text{ of } 100 \text{ grams} = 100 - 10 = 90 \text{ grams} \]

4. **Selling Price Calculation:**
- Let’s assume he sells the 100 grams for `x` rupees.
- The selling price for 90 grams is `x` rupees, which means the selling price per gram is:
\[ \text{Selling Price per gram} = \frac{x \text{ rupees}}{90 \text{ grams}} \]

5. **Profit Calculation:**
- The retailer earns a profit of `60%` on his cost price.
- Therefore, the selling price can also be expressed as:
\[ \text{Selling Price} = \text{Cost Price} + 60\% \text{ of Cost Price} = 100 + 60\% \text{ of } 100 = 100 + 60 = 160 \text{ rupees} \]

6. **Finding the Selling Price per Gram:**
- Since he sells 90 grams for 160 rupees:
\[ \text{Selling Price per gram} = \frac{160 \text{ rupees}}{90 \text{ grams}} \approx 1.78 \text{ rupees/gram} \]

7. **Markup Calculation:**
- The markup is calculated based on the cost price. The formula for markup percentage is:
\[ \text{Markup Percentage} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100 \]
- Plugging in the values:
\[ \text{Markup Percentage} = \left( \frac{160 - 100}{100} \right) \times 100 = \left( \frac{60}{100} \right) \times 100 = 60\% \]

### Conclusion:
The retailer marks up his goods by `60%`.