A dishonest dealer purchases goods at `20%` discount of the cost price of Rs x and also cheats his wholesaler by getting `20%` extra through false weighing, per kg. Then, he marks up his goods by `80%` of x, but he gives a discount of `25%` besides he cheats his customer by weighing `10%` less than the required. What is his overall profit percentage?

Options

A. `125%`
B. `100%`
C. `98.66%`
D. `120%`

Answer

To solve the problem step by step, we need to break down the transactions of the dishonest dealer and calculate the overall profit percentage.

### Step 1: Calculate the Cost Price (CP)
The dealer purchases goods at a 20% discount on the cost price (CP) of Rs x.
Let's assume the cost price (CP) is Rs 100 for simplicity.

- Discount = 20% of 100 = Rs 20
- Effective Cost Price (ECP) = 100 - 20 = Rs 80

**Hint:** Remember that the effective cost price is the price after applying the discount.

### Step 2: Calculate the Quantity Purchased
The dealer cheats his wholesaler by getting 20% extra through false weighing.

- Actual quantity he should receive = 1 kg = 1000 grams
- Extra quantity = 20% of 1000 grams = 200 grams
- Total quantity received = 1000 grams + 200 grams = 1200 grams

**Hint:** When calculating quantities, always consider the percentage increase or decrease carefully.

### Step 3: Calculate the Marked Price (MP)
The dealer marks up his goods by 80% of the cost price (CP).

- Marked Price (MP) = CP + 80% of CP = 100 + 80% of 100 = 100 + 80 = Rs 180

**Hint:** The marked price is the price before any discounts are applied.

### Step 4: Calculate the Selling Price (SP) after Discount
The dealer gives a discount of 25% on the marked price.

- Discount = 25% of 180 = Rs 45
- Selling Price (SP) = MP - Discount = 180 - 45 = Rs 135

**Hint:** Always subtract the discount from the marked price to find the selling price.

### Step 5: Calculate the Actual Quantity Sold
The dealer cheats his customer by weighing 10% less than the required amount.

- Actual quantity he should sell = 1000 grams
- Quantity sold = 1000 grams - 10% of 1000 grams = 1000 - 100 = 900 grams

**Hint:** Remember to adjust the quantity sold based on any cheating or discrepancies.

### Step 6: Calculate the Effective Selling Price per kg
Now, we need to find out how much he effectively sold per kg.

- Effective Selling Price per kg = SP / Quantity sold = 135 / 0.9 kg = Rs 150

**Hint:** When calculating effective prices, divide the total selling price by the actual quantity sold.

### Step 7: Calculate the Profit
Now we can calculate the profit made by the dealer.

- Cost Price for 900 grams = (80 / 1200) * 900 = Rs 60
- Selling Price for 900 grams = Rs 135
- Profit = Selling Price - Cost Price = 135 - 60 = Rs 75

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

### Step 8: Calculate the Overall Profit Percentage
Finally, we can calculate the overall profit percentage.

- Profit Percentage = (Profit / Cost Price) * 100
- Profit Percentage = (75 / 60) * 100 = 125%

**Hint:** To find the profit percentage, always divide the profit by the cost price and multiply by 100.

### Conclusion
The overall profit percentage of the dishonest dealer is **125%**.

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