Calculating Net Profit Percentage for a Dishonest Dealer

This problem involves calculating the net profit percentage of a dishonest dealer who uses two methods to increase profit: manipulating the price and using a faulty weighing balance.

Let's break down the process to find the net profit percentage.

Understanding the Profit Sources

The dealer makes profit from two sources:

1. Pricing Strategy: Marking up the price and then giving a discount.
2. Faulty Balance: Giving less quantity than what is paid for.

Effect of Pricing Strategy

Let's assume the dealer's Cost Price (CP) for a certain quantity (say, 1 kg or 1000 gm) is $C$.

• The dealer marks up the goods by 50%. So, the Marked Price (MP) is 50% more than the CP.

  MP = $\text{CP} \times \left(1 + \frac{50}{100}\right) = C \times \left(1 + 0.5\right) = 1.5C$

• The dealer then gives a discount of 20% on the Marked Price. So, the Selling Price (SP) based on the marked price is 20% less than the MP.

  SP = $\text{MP} \times \left(1 - \frac{20}{100}\right) = 1.5C \times \left(1 - 0.2\right) = 1.5C \times 0.80 = 1.2C$

So, based on the price manipulation alone, the dealer would charge $1.2C$ for goods that cost him $C$. This represents a 20% profit on the cost price if the quantity sold was exactly what was paid for.

Effect of Faulty Balance

The dealer uses a faulty balance which reads 1 kg (1000 gm) for 900 gm. This means when a customer pays for 1000 gm, they only receive 900 gm of the product.

This is where the second part of the profit comes from. The dealer's cost is for the quantity actually given (900 gm), but the revenue received is based on the quantity charged (1000 gm) at the marked-up and discounted price.

Combining Both Effects for Net Profit

Let's consider a transaction where a customer pays for 1 kg (1000 gm) of goods.

• The price the customer pays for 1000 gm is the Selling Price calculated earlier, which is $1.2C$, where $C$ is the dealer's cost for 1000 gm. This is the dealer's Revenue for this transaction.
• However, using the faulty balance, the dealer only gives the customer 900 gm of the product.
• What is the dealer's actual cost for this 900 gm? If the cost of 1000 gm is $C$, then the cost of 1 gm is $\frac{C}{1000}$.
• The cost of 900 gm is $\frac{C}{1000} \times 900 = 0.9 \times C = 0.9C$. This is the dealer's actual Cost for the goods sold in this transaction.

So, for a transaction where the dealer receives $1.2C$, his actual cost for the goods he gave away is $0.9C$.

The net profit for this transaction is:

Net Profit = Revenue - Cost of Goods Sold

Net Profit = $1.2C - 0.9C = 0.3C$

Calculating Net Profit Percentage

The net profit percentage is calculated on the actual cost of the goods sold.

Net Profit Percentage = $\left(\frac{\text{Net Profit}}{\text{Actual Cost of Goods Sold}}\right) \times 100\%$

Net Profit Percentage = $\left(\frac{0.3C}{0.9C}\right) \times 100\%$

Net Profit Percentage = $\left(\frac{0.3}{0.9}\right) \times 100\%$

Net Profit Percentage = $\left(\frac{3}{9}\right) \times 100\% = \left(\frac{1}{3}\right) \times 100\%$

Net Profit Percentage = $33.333...\%$

Rounding Off

The question asks for the net profit percentage rounded off to the nearest integer.

$33.333...\%$ rounded to the nearest integer is 33%.

Thus, the dealer's net profit percentage is 33%.

Revision Table: Dishonest Dealer Profit Calculation

Additional Information: Profit and Loss with Faulty Weights

Problems involving faulty weights or measures are common in profit and loss calculations. The key is to understand the actual quantity of goods the dealer is buying (at cost price) and the actual quantity of goods they are selling (for the selling price received from the customer).

A faulty balance that reads 'X' for 'Y' (where Y < X) means the dealer is selling Y quantity while charging for X quantity. This effectively increases the selling price per unit quantity, or decreases the cost price for the quantity they charge for.

When combined with price changes (mark-up, discount), you calculate the final price charged for the quantity the customer thinks they are getting, and compare it to the cost price of the quantity the dealer actually gives.

The net profit percentage is always calculated on the actual cost incurred by the dealer for the goods that are transferred to the customer.