The printed price of a home theatre set is Rs. 4,950. If two successive discounts of 20% and 15% are offered on this marked price, what is the final selling price of the home theatre?

Introduction / Context:
This problem is a straightforward application of successive discounts on a marked price. The home theatre has a listed price, and the seller offers two discounts, one after the other. We need to compute the final selling price after both discounts are applied. Such questions are basic in the discount and profit and loss chapter and reinforce the multiplicative nature of successive percentage changes.

Given Data / Assumptions:

• Marked price (MP) of the home theatre = Rs. 4,950.
• First discount = 20% on the marked price.
• Second discount = 15% on the reduced price after the first discount.
• We need to find the final selling price.

Concept / Approach:
Successive discounts are not added directly; instead, each discount is applied sequentially to the current price. A discount of d% means we multiply the current price by (1 − d/100). Therefore, with discounts of 20% and 15% applied successively, the final price factor is 0.80 * 0.85. Multiplying this combined discount factor by the marked price gives the final selling price.

Step-by-Step Solution:
Marked price MP = Rs. 4,950.After the first discount of 20%, price becomes MP * (1 − 20/100) = 4950 * 0.80.Compute: 4950 * 0.80 = Rs. 3,960.After the second discount of 15%, price becomes 3960 * (1 − 15/100) = 3960 * 0.85.Calculate: 3960 * 0.85 = 3,960 * 85 / 100 = 336,600 / 100 = Rs. 3,366.Thus, the final selling price is Rs. 3,366.

Verification / Alternative check:
We can also compute the combined multiplier directly: 0.80 * 0.85 = 0.68.Final price = 4950 * 0.68.Compute: 4950 * 0.68 = 4950 * 68 / 100 = (4950 * 68) / 100 = 336,600 / 100 = Rs. 3,366.Both methods produce the same final selling price.

Why Other Options Are Wrong:
Rs. 6,633 and Rs. 6,363 are greater than the marked price and therefore cannot be the result of discounts.Rs. 3,636 would correspond to a different pair or order of discounts and does not match the exact calculation.Only Rs. 3,366 matches the correct compounded discount result.

Common Pitfalls:
A frequent mistake is to add the discounts directly (20% + 15% = 35%) and apply a single 35% discount, which is incorrect.Another error is applying the second discount to the original marked price instead of the reduced price.Students sometimes miscalculate the decimal equivalents, using 0.2 and 0.15 incorrectly.

Final Answer:
The final selling price of the home theatre set is Rs. 3,366.