A shopkeeper marks up his goods by 80% above cost price and then offers a discount of 20% on the marked price. If the cost price of the article is Rs. 450, what is the final selling price?

Introduction / Context:
This question combines both markup and discount in a single transaction, which is very common in real life. A shopkeeper increases the price of an item above its cost price (markup) and later offers a discount to attract buyers. The effective selling price depends on both of these percentage changes. Aptitude exams often test whether you know that markup and discount are applied one after the other on different bases, not simply added or subtracted as raw percentages.

Given Data / Assumptions:
- Cost price of the article = Rs. 450. - Markup percentage above cost price = 80%. - Discount percentage on marked price = 20%. - We need the final selling price after both operations. - There are no extra taxes or hidden charges.

Concept / Approach:
First compute the marked price using Marked Price = Cost Price * (1 + Markup Percentage / 100). Then apply the discount to the marked price using Selling Price = Marked Price * (1 - Discount Percentage / 100). It is crucial to note that markup is calculated on the cost price, while discount is calculated on the marked price. You cannot simply subtract 20% from 80% to say the net percentage is 60%, because the bases are different in each step.

Step-by-Step Solution:
Step 1: Compute the marked price (MP). Step 2: MP = 450 * (1 + 80 / 100) = 450 * 1.80. Step 3: MP = 810 rupees. Step 4: Apply 20% discount on the marked price to get selling price (SP). Step 5: SP = MP * (1 - 20 / 100) = 810 * 0.80. Step 6: SP = 648 rupees. Step 7: So the article finally sells for Rs. 648.

Verification / Alternative check:
To verify logically, calculate the effective factor of these two successive changes. Markup factor is 1.80 and discount factor is 0.80. The combined factor is 1.80 * 0.80 = 1.44. This factor acts directly on the cost price. Thus effective selling price = 450 * 1.44 = 648, which matches our earlier result. Therefore both the stepwise and combined-factor methods give the same answer, confirming that the calculations are reliable.

Why Other Options Are Wrong:
Rs. 548, Rs. 748, and Rs. 848 correspond to incorrect combinations of percentages or to mistakes such as subtracting discount from markup directly, or applying discount on cost price instead of marked price. For example, if someone incorrectly applied discount on cost price, they might compute 450 * 0.80 = 360 and then attempt to reapply markup, which is wrong. Only Rs. 648 respects the correct order and bases of these percentage operations.

Common Pitfalls:
Many students incorrectly think that an 80% markup and 20% discount give a net 60% increase, but this is not accurate because the discount is applied on the higher marked price, not on the cost price. Another pitfall is using the wrong base for percentage calculations or mixing up cost price, marked price and selling price. Always process the steps in order: first markup on cost price, then discount on marked price.

Final Answer:
The final selling price of the article after an 80% markup and 20% discount on a cost price of Rs. 450 is Rs. 648.