This question asks us to calculate the overall percentage profit for a dishonest dealer. The dealer employs two deceptive tactics: selling goods at a loss concerning the cost price and providing less weight than stated.

Understanding the Dealer's Deception

A dishonest dealer uses tricks to make a profit. In this case, the dealer:

• Sells goods claiming a 7% loss on the cost price.
• Actually provides 18% less weight than what the customer pays for.

We need to find the net percentage profit the dealer makes after applying both these strategies.

Setting a Baseline Cost Price

To easily track the profit, let's assume the dealer buys a certain quantity of goods for a Cost Price (CP) of $100$. This value acts as our base for calculations.

• Assumed Cost Price (CP) = $100$.

Calculating the Selling Price (SP)

The dealer sells the goods at a 7% loss on the cost price. This means the Selling Price (SP) is set lower than the CP.

• Loss Amount = $7\%$ of CP = $\frac{7}{100} \times 100 = 7$.
• Selling Price (SP) = CP - Loss Amount = $100 - 7 = 93$.
• Alternatively, we can calculate the SP directly: $SP = CP \times (1 - \frac{\text{Loss}\%}{100})$ $SP = 100 \times (1 - \frac{7}{100})$ $SP = 100 \times (1 - 0.07)$ $SP = 100 \times 0.93 = 93$.

The dealer receives $93$ for the transaction, based on the quantity the customer believes they are receiving.

Accounting for Reduced Weight

The dealer cheats the customer by providing less weight. The dealer uses 18% less weight than what the price corresponds to.

• Percentage reduction in weight = $18\%$.
• The actual weight provided is $(100\% - 18\%) = 82\%$ of the intended weight.

Determining the Actual Cost Price (CP_actual)

Since the dealer provides only 82% of the intended weight, the cost incurred by the dealer for the goods actually sold is 82% of the initial assumed cost price.

• Actual Cost Price (CP_actual) = $82\%$ of the initial CP
• $CP_{actual} = \frac{82}{100} \times 100 = 82$.

So, the goods the dealer actually gave to the customer cost the dealer $82$.

Calculating the Dealer's Profit

The profit is the difference between the selling price (the money the dealer receives) and the actual cost price (the money the dealer spent on the goods provided).

• Profit = Selling Price (SP) - Actual Cost Price (CP_actual)
• Profit = $93 - 82 = 11$.

The dealer makes a profit of $11$.

Calculating the Percentage Profit

The percentage profit is calculated based on the Actual Cost Price incurred by the dealer.

• Percentage Profit = $\frac{\text{Profit}}{\text{Actual CP}} \times 100$
• Percentage Profit = $\frac{11}{82} \times 100$
• Percentage Profit = $\frac{1100}{82}$
• Percentage Profit $\approx 13.414634... \%$.

Rounding this to two decimal places gives us the final answer.

• Percentage Profit $\approx 13.41\%$.

Therefore, the dishonest dealer makes a profit of approximately 13.41%.