A dealer marks his goods 20 percent above the cost price and then allows a discount on the marked price so that his net profit is 8 percent. What is the rate of discount?

Introduction / Context:
This question combines markup and discount concepts applied on cost price and marked price. It is important to understand which percentage is applied to which base. Many students confuse profit percentage with discount percentage, so a clear stepwise calculation is essential.

Given Data / Assumptions:

• Goods are marked 20 percent above cost price.
• Some discount is given on the marked price.
• Net profit obtained by the dealer is 8 percent on cost price.
• We are asked to find the discount rate.

Concept / Approach:
First express the marked price in terms of the cost price using the markup. Then express the selling price using the profit percentage. Finally relate selling price to marked price using a discount factor and solve for the discount rate. All calculations are easier if we assume a convenient cost price like 100 units.

Step-by-Step Solution:
Let cost price = 100 units.Marked price = cost price * 1.20 = 120 units.Required profit = 8 percent, so selling price = 100 * 1.08 = 108 units.Let discount rate be d percent on marked price.Then selling price = marked price * (1 - d/100) = 120 * (1 - d/100).So 120 * (1 - d/100) = 108, therefore (1 - d/100) = 108 / 120 = 0.9.Hence d/100 = 0.1 and discount rate d = 10 percent.

Verification / Alternative check:
With 10 percent discount on marked price of 120, the selling price becomes 120 * 0.9 = 108. Since cost price is 100, profit is 8 units, which is 8 percent of 100. This confirms the correctness of our calculation.

Why Other Options Are Wrong:
Discounts like 12 percent, 6 percent and 4 percent produce selling prices that do not correspond to exactly 8 percent profit on cost price. For each wrong discount, the selling price either gives less or more than 8 percent profit.

Common Pitfalls:
One common mistake is to subtract profit percent directly from markup percent (20 minus 8) and assume 12 percent is the discount. This is wrong because markup and discount are applied on different bases. Always convert everything to actual rupee or unit values from a chosen cost price before solving.

Final Answer:
The rate of discount is 10 percent.