The original price of a television set is Rs. 6000. Its price is first discounted by 20% and then the reduced price is increased by 10% as a service charge. What is the final price charged by the shopkeeper?

Introduction / Context:
Successive percentage changes on prices are very common in real life, especially when shops offer discounts and then add service charges or taxes. This question asks you to apply two percentage operations in sequence to the original price of a television. It tests the understanding that these operations act on the current price at each step, and not directly on the original amount for both steps together.

Given Data / Assumptions:

• Original price of the television set = Rs. 6000.
• First change: a discount of 20% on the original price.
• Second change: an increase of 10% on the discounted price as a service contract charge.
• We have to calculate the final price that the customer pays.

Concept / Approach:
When a discount or increment is applied successively, we must apply each percentage change to the price that exists at that stage. The general idea is: new price after first change = original price * (1 minus discount rate). Then, the new price after the second change = previous price * (1 plus increase rate). We should avoid the mistake of trying to directly add or subtract the percentages because they are applied on different bases.

Step-by-Step Solution:
Step 1: Calculate the price after a 20% discount on Rs. 6000. Step 2: A 20% discount means the customer pays 80% of the original amount. So discounted price = 6000 * (80 / 100). Step 3: Compute 6000 * (80 / 100) = 6000 * 0.8 = Rs. 4800. Step 4: Now a 10% increase is applied on this discounted price of Rs. 4800. Step 5: A 10% increase corresponds to multiplying by 1.10. So final price = 4800 * 1.10. Step 6: Calculate 4800 * 1.10 = 5280. Step 7: Therefore, the price charged by the shopkeeper is Rs. 5280.

Verification / Alternative check:
Instead of two separate steps, we can think in terms of combined multiplication factors. First factor: 80% or 0.8. Second factor: 110% or 1.10. Overall factor = 0.8 * 1.10 = 0.88. Therefore final price = 6000 * 0.88 = 5280, which matches our previous answer. This confirms that our calculations are consistent and the method is correct.

Why Other Options Are Wrong:
Rs. 5400 is higher than the correct final amount and would correspond to a different combination of percentage changes. Rs. 5100 is also not consistent with applying 20% discount followed by 10% increase. Rs. 4200 is even less, and would imply a much larger effective discount. None of these values match the actual stepwise computation, so they are incorrect.

Common Pitfalls:
A frequent mistake is to add 20% and 10% to get 30% and then assume a single net change. However, 20% discount and 10% increase do not cancel or simply add, because they are applied on different amounts. Another error is miscalculating percentages of large numbers under time pressure. Carefully writing the intermediate price after each step prevents such confusion.

Final Answer:
The final price charged by the shopkeeper is Rs. 5280.