Question

A dishonest dealer sells his goods at 10% loss on cost price and uses 30% less weight. What is his profit or loss percentage?

• A. \(28\frac{4}{7}\%\ \text{loss}\)
• B. \(28\frac{3}{7}\%\ \text{profit}\)
• C. \(28\frac{3}{7}\%\ \text{loss}\)
• D. \(28\frac{4}{7}\%\ \text{profit}\)

Answer 1

The Correct Option is D

To solve this problem, we need to calculate the overall profit or loss percentage considering both the selling price and the use of less weight.

First, let's assume the cost price of 1 kg of goods is \(x\).

The dealer sells his goods at a 10% loss on cost price, meaning he sells them for 90% of the cost price:

\(\text{Selling Price of 1 kg} = 0.9x\)

However, he uses 30% less weight than supposed, so he sells only 70% of the weight.

This means he charges for 1 kg but actually sells only 0.7 kg.

Now, calculate the effective selling price for this 0.7 kg of goods:

The cost price of 0.7 kg = \(0.7x\)

The selling price for 1 kg is \(0.9x\). Therefore, the profit is calculated on 0.7 kg sold:

Profit amount for selling 0.7 kg at the price of 0.9 kg:

\(\text{Profit} = 0.9x - 0.7x = 0.2x\)

Profit Percentage is calculated using the formula:

\(\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price for 0.7 kg}} \right) \times 100\)

Therefore,

\(\text{Profit Percentage} = \left( \frac{0.2x}{0.7x} \right) \times 100 = \frac{2}{7} \times 100\)

\(\text{Profit Percentage} = 28\frac{4}{7}\%\)

Thus, the dealer makes a net profit of \(28\frac{4}{7}\%\).

The correct answer, therefore, is \(28\frac{4}{7}\%\ \text{profit}\).