A shopkeeper sells a table at a 20% discount on its marked price and still earns a profit of 60%. If he sells the same table at a 40% discount on the marked price, what will be his new profit percentage?

Introduction / Context:
This question focuses on the relation between marked price, cost price and selling price when discounts are involved. It is a classic profit and loss problem where the discount is changed, and we are asked to find how the profit percentage changes. Understanding how marked price acts as a bridge between cost price and selling price is crucial in such problems.

Given Data / Assumptions:

• The table has some marked price, say MP.
• At 20% discount on MP, the shopkeeper still makes 60% profit.
• We need to find the profit percentage when the discount becomes 40% on the same MP.
• Cost price of the table remains the same in both situations.

Concept / Approach:
We use the relations SP = MP * (1 - discount_percent / 100) and SP = CP * (1 + profit_percent / 100). First we relate the 20% discount and 60% profit to form an equation involving MP and CP. From that, we find MP in terms of CP. Then we find the new SP with 40% discount on MP and compute the new profit percentage using the same CP.

Step-by-Step Solution:
Let cost price of the table be CP and marked price be MP.When discount is 20%, SP1 = MP * 0.80.Given profit at this stage is 60%, so SP1 = CP * 1.60.So, MP * 0.80 = 1.60 * CP, therefore MP = (1.60 / 0.80) * CP = 2 * CP.Now discount is 40%, so new selling price SP2 = MP * 0.60 = 2 * CP * 0.60 = 1.20 * CP.Profit percentage in this case = ((SP2 - CP) / CP) * 100 = ((1.20 * CP - CP) / CP) * 100 = 20%.

Verification / Alternative check:
Assume a convenient cost price, for example CP = Rs 100. Then MP = Rs 200. With 20% discount, SP1 = 200 * 0.80 = Rs 160 which is a 60% profit on Rs 100. With 40% discount, SP2 = 200 * 0.60 = Rs 120. Profit is Rs 20 on cost Rs 100, that is exactly 20%, which confirms our earlier algebraic solution.

Why Other Options Are Wrong:
30%, 35% and 40% would all require higher selling prices than Rs 120 when CP is Rs 100. Since the new SP comes directly from applying 40% discount on the same marked price, none of these higher profit percentages match the computed value. Only 20% is consistent with both the discount and the cost price relationships.

Common Pitfalls:
Many students mistakenly apply discount directly on cost price or assume that profit percentage decreases by the same percentage as the increase in discount. In reality, discounts work on marked price and profits work on cost price. Keeping these roles separate prevents confusion and mistakes in multi step problems like this.

Final Answer:
The new profit percentage when the discount is 40% is 20%.