A merchant marks his wares 30% more than the real price and allows 20%…

Concept: The net profit or loss percentage after a mark-up followed by a discount is NOT simply mark-up% minus discount%. It must be found via the effective selling price: SP = CP x (1 + mark-up%) x (1 - discount%), and Profit% = ((SP - CP) / CP) x 100.

Application:

1. Let the cost price (CP) = Rs 100.

2. Marked Price (MP) = CP + 30% of CP = 100 + 30 = Rs 130.

3. A discount of 20% is allowed on the marked price: discount amount = 20% of 130 = Rs 26.

4. Selling Price (SP) = MP - discount = 130 - 26 = Rs 104.

5. Profit = SP - CP = 104 - 100 = Rs 4.

6. Profit% = (Profit / CP) x 100 = (4 / 100) x 100 = 4%.

Cross-check: Using the direct successive-change formula, net% change = m - d - (m*d/100), where m = 30 and d = 20, so 30 - 20 - (30*20/100) = 10 - 6 = 4%, matching the step-by-step calculation above.