A shopkeeper sold two items. The selling price of the first item equals the cost price of the second item. He sold the first item at a profit of 25% and the second item at a loss of 12%. What is the overall profit or loss percentage?

Given:

Selling price of the first item (SP1) = Cost price of the second item (CP2)

Profit on the first item = 25%

Loss on the second item = 12%

Formula Used:

Profit = Selling Price - Cost Price

Profit % = (Profit / Cost Price) × 100

Loss = Cost Price - Selling Price

Loss % = (Loss / Cost Price) × 100

Calculation:

Let the cost price of the first item be CP1.

Selling price of the first item (SP1) = CP1 + 25% of CP1 = CP1 + 0.25 × CP1 = 1.25 × CP1

Given SP1 = CP2, so CP2 = 1.25 × CP1

Selling price of the second item (SP2) = CP2 - 12% of CP2 = CP2 - 0.12 × CP2 = 0.88 × CP2

Substitute CP2 = 1.25 × CP1 in the equation for SP2:

SP2 = 0.88 × (1.25 × CP1) = 1.1 × CP1

Total Cost Price (TCP) = CP1 + CP2 = CP1 + 1.25 × CP1 = 2.25 × CP1

Total Selling Price (TSP) = SP1 + SP2 = 1.25 × CP1 + 1.1 × CP1 = 2.35 × CP1

Overall Profit = TSP - TCP = 2.35 × CP1 - 2.25 × CP1 = 0.10 × CP1

Overall Profit Percentage = (Overall Profit / Total Cost Price) × 100

Overall Profit Percentage = (0.10 × CP1 / 2.25 × CP1) × 100

Overall Profit Percentage = (0.10 / 2.25) × 100

Overall Profit Percentage = (10 / 225) × 100

Overall Profit Percentage = 40 / 9 = 4\(\frac{4}{9}\)

The overall profit percentage is 4\(\frac{4}{9}\)%.