ITC sells one product at a profit of 20% and another product at a loss of 20%, both at the same selling price. What overall percentage loss does ITC incur on these two products taken together?

Introduction / Context:
This is a classic misconception question about profit and loss. Many people incorrectly think that a 20% profit on one item and a 20% loss on another item of the same value cancel out. However, when the selling prices or cost prices differ, the percentages do not simply cancel. This problem emphasizes that profit and loss percentages must be considered on the correct base, usually the cost price.

Given Data / Assumptions:

• One product is sold at a profit of 20%.
• Another product is sold at a loss of 20%.
• Both products have the same selling price.
• We need the net percentage loss or gain for ITC on these two products combined.

Concept / Approach:
Let the common selling price of each product be S. Using the given profit and loss percentages, we can find the cost price for each product. Once the individual cost prices are known, we add them to get total cost and add the selling prices to get total revenue. From there, net profit or loss percentage is computed as (total SP - total CP) / total CP * 100. The key is to recognize that equal percentage profit and loss on different bases do not cancel out.

Step-by-Step Solution:
Step 1: Let selling price of each product = S.Step 2: For the first product with 20% profit, SP = 1.2 * CP₁ ⇒ CP₁ = S / 1.2.Step 3: For the second product with 20% loss, SP = 0.8 * CP₂ and SP is same S, so S = 0.8 * CP₂ ⇒ CP₂ = S / 0.8.Step 4: Total cost price = CP₁ + CP₂ = S/1.2 + S/0.8.Step 5: Compute: S/1.2 = (5/6)S and S/0.8 = (5/4)S. So total CP = (5/6 + 5/4)S = (10/12 + 15/12)S = (25/12)S.Step 6: Total selling price = S + S = 2S.Step 7: Net loss = total CP - total SP = (25/12)S - 2S = (25/12 - 24/12)S = (1/12)S.Step 8: Loss % = (loss / total CP) * 100 = ((1/12)S) / ((25/12)S) * 100 = (1/25) * 100 = 4%.

Verification / Alternative check:
To see it numerically, assume S = Rs 120. Then CP₁ = 120 / 1.2 = Rs 100. For the second product, CP₂ = 120 / 0.8 = Rs 150. Total CP = 100 + 150 = Rs 250. Total SP = 120 + 120 = Rs 240. Net loss = 10, and loss% = (10 / 250) * 100 = 4%. This concrete example confirms the algebraic result of 4% loss.

Why Other Options Are Wrong:
0% is the common misconception that equal gain and loss percentages cancel out. 1% and 2% represent partial miscalculations of the base or mixing the two percentages directly without considering total cost. Only 4% correctly represents the net loss when both transactions are combined using proper cost bases.

Common Pitfalls:
The biggest pitfall is thinking that profit% and loss% are simple numbers that can be averaged, ignoring that they apply to different cost prices. Another error is taking the average of +20% and -20% as 0% and concluding there is no gain or loss. Always compute total cost and total selling price explicitly when multiple transactions are involved.

Final Answer:
ITC incurs a net loss of 4% on the two products combined.