Trader's Profit Calculation Explained

This problem involves calculating the overall profit percentage when a trader uses two deceptive methods: first, by claiming a profit margin, and second, by using a faulty weight that is lighter than indicated.

Marked Price Based on Claimed Profit

Let's assume the cost price (CP) for a certain quantity of pulses (e.g., 100 grams) is Rs. 100.

The trader claims to sell at a profit of 3%. This means the marked price (MP) is set higher than the cost price to include this intended profit. If the weight were accurate, the selling price for 100 grams would be:

$MP_{intended} = CP \times (1 + \text{Profit Percentage})$

$MP_{intended} = 100 \times (1 + 0.03) = 100 \times 1.03 = 103$

So, the trader marks the price as Rs. 103 for 100 grams.

Impact of Dishonest Weight

The trader dishonestly uses a weight that is 15% less than what is mentioned on the scale.

This means when the scale shows 100 grams, the actual weight of pulses given to the customer is:

$Actual Weight = Marked Weight \times (1 - \text{Percentage Defect})$

$Actual Weight = 100 \text{ grams} \times (1 - 0.15) = 100 \times 0.85 = 85 \text{ grams}$

Actual Cost Price vs. Selling Price

Now, we need to determine the trader's actual profit based on the cost incurred and the price received.

• Actual Cost Price (CP): The trader's cost is based on the actual amount of pulses (85 grams) they provide. Since the cost of 100 grams is Rs. 100, the cost of 1 gram is Rs. 1. Therefore, the cost for 85 grams is:

  $Actual CP = 85 \text{ grams} \times \text{Rs. } 1/\text{gram} = \text{Rs. } 85$

• Selling Price (SP): The trader charges the customer based on the weight shown on the scale (100 grams) at the marked price rate (Rs. 103 for 100 grams). Even though only 85 grams are given, the trader collects the price for 100 grams.

  $SP = \text{Rs. } 103$

Calculating Total Profit Percentage

The total profit is the difference between the selling price and the actual cost price.

$Profit = SP - Actual CP$

$Profit = \text{Rs. } 103 - \text{Rs. } 85 = \text{Rs. } 18$

To find the total percentage profit, we compare this profit to the actual cost price incurred by the trader:

$Total Percentage Profit = (\text{Profit} / \text{Actual CP}) \times 100\%$

$Total Percentage Profit = (18 / 85) \times 100\%$

$Total Percentage Profit \approx 21.176...\%$

Rounding this to the nearest whole number, the total percentage profit is 21%.