Profit and Loss – Markup and target profit: A dealer marks his goods 20% above cost price. After allowing a discount he realizes an 8% profit. What rate of discount did he allow on the marked price?

Introduction / Context:
We relate cost price, marked price, selling price, and discount rate. Markup is applied over CP; discount is applied on MP.

Given Data / Assumptions:

• MP = 1.20 * CP
• SP = 1.08 * CP
• Let discount rate be d

Concept / Approach:
SP = (1 - d) * MP. Substitute MP and SP in terms of CP and solve for d.

Step-by-Step Solution:
1.08 * CP = (1 - d) * 1.20 * CP1 - d = 1.08 / 1.20 = 0.90d = 0.10 = 10%

Verification / Alternative check:
Assume CP = 100; MP = 120; with 10% discount SP = 108, which is 8% over CP.

Why Other Options Are Wrong:
12%, 6%, 4%, 14% do not yield SP = 1.08 * CP.

Common Pitfalls:
Subtracting percentages directly instead of using the relationship through MP.

Final Answer:
10%