A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the customer, Besides, he also cheats both his supplier and his buyer by 100 grams while buying of selling 1 kilogram. Find the percentage profit earned by the shopkeeper?

Options

A. `20%`
B. `25%`
C. `32%`
D. `27.5%`

Answer

To find the percentage profit earned by the dishonest dealer, we need to analyze the situation step by step.

### Step 1: Understanding the Markup and Discount
1. **Markup of 20%**:
- Let the cost price (CP) of the goods be \( 100 \) (for simplicity).
- The selling price (SP) after a 20% markup is:
\[ SP = CP + 20\% \text{ of } CP = 100 + 20 = 120 \]

2. **Discount of 10%**:
- The dealer gives a 10% discount on the marked price (SP).
- The discount amount is:
\[ \text{Discount} = 10\% \text{ of } 120 = 12 \]
- Therefore, the selling price after discount is:
\[ SP_{\text{after discount}} = 120 - 12 = 108 \]

### Step 2: Adjusting for Cheating in Weight
3. **Cheating by 100 grams**:
- The dealer cheats by giving only 900 grams when selling 1 kilogram (1000 grams).
- Therefore, when he sells 1 kg (1000 grams), he actually sells only 900 grams.
- This means the effective selling price per kg becomes:
\[ \text{Effective SP} = \frac{SP_{\text{after discount}}}{\text{actual weight sold}} = \frac{108}{0.9} = 120 \]

### Step 3: Adjusting for Cheating in Purchase
4. **Cheating while buying**:
- When the dealer buys 1 kg (1000 grams), he actually receives 1100 grams due to cheating.
- Therefore, the effective cost price (CP) per kg becomes:
\[ \text{Effective CP} = \frac{CP}{\text{actual weight bought}} = \frac{100}{1.1} \approx 90.91 \]

### Step 4: Calculating Profit
5. **Calculating Profit**:
- The profit earned by the dealer is:
\[ \text{Profit} = \text{Effective SP} - \text{Effective CP} = 120 - 90.91 \approx 29.09 \]

### Step 5: Calculating Percentage Profit
6. **Calculating Percentage Profit**:
- The percentage profit is given by:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Effective CP}} \right) \times 100 = \left( \frac{29.09}{90.91} \right) \times 100 \approx 32\% \]

### Final Answer
The percentage profit earned by the shopkeeper is approximately **32%**.

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