Understanding the Problem

This question asks us to calculate the total profit percentage earned by a trader. The trader uses two methods to increase profit: claiming a higher profit margin than the actual cost price and using a weighing scale that shows a higher weight than what is actually given to the customer (underweight).

Calculating Profit from Claimed Margin

The trader claims to sell pulses at a profit of 48%. Let's assume the cost price (CP) of the pulses is $100$.

The selling price (SP) based on this claim would be:

$ \text{SP}_{\text{claimed}} = \text{CP} \times (1 + \text{Profit Percentage}/100) $

$ \text{SP}_{\text{claimed}} = 100 \times (1 + 48/100) $

$ \text{SP}_{\text{claimed}} = 100 \times (1 + 0.48) $

$ \text{SP}_{\text{claimed}} = 100 \times 1.48 = 148 $

So, the trader intends to sell goods worth $100$ for $148$.

Calculating Profit from Dishonest Weight

The trader uses a weight that is 12% less than what is mentioned. This means when the scale shows 100 units (e.g., 100 grams or 100 kg), the trader actually gives only $100 - 12 = 88$ units.

The trader sells these 88 units of goods at the price intended for 100 units, which is $148$ (as calculated above).

Determining Actual Cost Price and Selling Price

• The actual cost price (CP) for the goods the trader gives is the cost of 88 units, which is $88$.
• The actual selling price (SP) received by the trader is the price for 100 units, which is $148$.

Calculating the Total Profit Percentage

Now we can calculate the actual profit and the profit percentage based on the actual cost price.

Actual Profit = Actual SP - Actual CP

Actual Profit = $148 - 88 = 60$

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

Total Profit Percentage = $ (60 / 88) \times 100 $

To simplify the fraction $60/88$, we can divide both numerator and denominator by their greatest common divisor, which is 4:

$ \frac{60}{88} = \frac{60 \div 4}{88 \div 4} = \frac{15}{22} $

Now, calculate the percentage:

Total Profit Percentage = $ \frac{15}{22} \times 100 $

Total Profit Percentage = $ \frac{1500}{22} $

Total Profit Percentage $\approx 68.1818... \%$

Rounding the Answer

The question asks to round the answer to the nearest whole number.

Rounding $68.1818... \%$ to the nearest whole number gives $68\%$.

Conclusion

By combining the claimed profit margin and the dishonest underweight measure, the trader earns a total profit of approximately 68%.