Understanding the Trader's Profit Scenario

This problem requires calculating the overall profit percentage for a trader who employs two strategies to maximize earnings: claiming a higher profit margin and using a faulty weighing scale.

• Claimed Profit: The trader announces a profit of 52%. This implies they intend to sell goods at a price 52% higher than their cost.
• Dishonest Weight: The trader uses a scale that shows a measurement 8% less than the actual weight. This means if the scale indicates 100 units, the customer receives only 92 units (100 - 8% of 100).

The goal is to determine the true total profit percentage earned by the trader, considering both the markup and the underweight.

Step-by-Step Profit Calculation

To simplify calculations, let's assume the cost price (CP) of 1 unit of weight (e.g., 1 gram or 1 kilogram) is '$ C $'.

1. Calculate the Intended Selling Price (SP)

Based on the claimed profit of 52%, the trader sets an intended selling price. If the weight were accurate, the SP for a given quantity would be:

Intended SP = $ C \times (1 + \frac{52}{100}) = C \times (1 + 0.52) = 1.52 \times C $

2. Incorporate the Effect of the Dishonest Weight

The trader uses a scale that provides 8% less weight. Let's analyze the situation assuming the scale indicates '100 units' for sale.

• Actual Cost Price (CP): The trader only delivers 92 units (which is $100 - 8 = 92$ units). The cost incurred by the trader is for these 92 units.
  Actual CP = $ 92 \times C $
• Actual Selling Price (SP): The customer pays the price based on the scale showing 100 units, which is marked up according to the trader's claim. The intended selling price for 100 units is calculated based on the cost of 100 units ($ 100 \times C $).
  Intended SP for 100 units = $ (100 \times C) \times (1 + \frac{52}{100}) = (100 \times C) \times 1.52 = 152 \times C $.
  This amount, $ 152 \times C $, is what the trader actually receives from the customer, even though they are only providing 92 units of weight.

3. Determine the Actual Profit

The actual profit is the difference between the amount the trader receives (Actual SP) and the cost incurred for the goods provided (Actual CP).

• Actual Selling Price = $ 152 \times C $
• Actual Cost Price = $ 92 \times C $
• Actual Profit = Actual SP - Actual CP
  Actual Profit = $ (152 \times C) - (92 \times C) $
  Actual Profit = $ (152 - 92) \times C = 60 \times C $

4. Calculate the Total Profit Percentage

The total profit percentage is calculated using the Actual Cost Price as the base.

Total Profit Percentage = $ (\frac{\text{Actual Profit}}{\text{Actual Cost Price}}) \times 100 $

Substituting the values we found:

Total Profit Percentage = $ (\frac{60 \times C}{92 \times C}) \times 100 $

The '$ C $' term cancels out:

Total Profit Percentage = $ (\frac{60}{92}) \times 100 $

Simplify the fraction:

Total Profit Percentage = $ (\frac{15}{23}) \times 100 $

Performing the division:

Total Profit Percentage $ \approx 65.217\% $

5. Round the Result

The question asks for the answer rounded to the nearest whole number.

Rounded Profit Percentage = 65%