A dealer sells his goods at 22% loss on cost price but uses 44% less weight. What is his percentage profit or loss?

Given:

Stated loss on cost price = 22%

Less weight used = 44%

Formula Used:

Actual goods sold = Claimed goods - (Percentage less weight × Claimed goods)

Selling Price (SP) = Cost Price (CP) × (1 - Loss Percentage/100)

Percentage Profit = \(\frac{\text{Actual SP - Actual CP}}{\text{Actual CP}}\) × 100

Calculations:

Let's assume the dealer's cost price for 100 units of weight is ₹100.

⇒ Actual Cost Price (CP) for 1 unit of weight = ₹1

The dealer claims to sell at a 22% loss on cost price. This means for goods he claims to sell for ₹100 (which cost him ₹100), he sells them for:

SP = CP - 22% of CP

SP = 100 - \(\frac{22}{100}\) × 100

SP = 100 - 22 = ₹78

So, the dealer receives ₹78 for the quantity of goods he claims to sell (e.g., for 100 units if we consider it in terms of money equivalent of weight).

The dealer uses 44% less weight. This means if he claims to sell 100 units of weight, he actually gives:

Actual weight given = 100 - 44% of 100

Actual weight given = 100 - 44 = 56 units of weight

Since the cost price of 1 unit of weight is ₹1, the actual cost of 56 units of weight given is:

Actual CP = 56 units × ₹1/unit = ₹56

The dealer effectively sold 56 units of goods (Actual CP = ₹56) for ₹78 (Effective SP).

Since Effective SP (₹78) > Actual CP (₹56), it's a profit.

Profit = Effective SP - Actual CP

Profit = 78 - 56 = ₹22

Percentage Profit = \(\frac{\text{Profit}}{\text{Actual CP}}\) × 100

Percentage Profit = \(\frac{22}{56}\) × 100

Percentage Profit = \(\frac{11}{28}\) × 100

Percentage Profit = \(\frac{275}{7}\) = \(39\frac{2}{7}\%\)

∴ The dealer makes a profit of approximately\(39\frac{2}{7}\%\)