Mr. X bought a music system at a 20% discount on the labelled (marked) price. If, instead, he had received a 25% discount, he would have saved ₹500 more. At what price did he actually buy the music system (i.e., the amount he paid after 20% discount)?

Introduction / Context:
This discount-comparison problem asks for the actual amount paid when a 20% discount is applied. The key idea is that the difference between a 25% discount and a 20% discount equals 5% of the labelled price, which is given numerically as ₹500. Once the marked price is found, we compute the paid price at 20% off.

Given Data / Assumptions:

• Let labelled (marked) price = M rupees.
• Scenario A (given): discount = 20% → paid = 0.80 * M.
• Scenario B (hypothetical): discount = 25% → paid = 0.75 * M.
• Extra saving if 25% were given instead of 20% = ₹500.

Concept / Approach:
The “extra saving” is exactly the difference in discounts: 25% − 20% = 5% of M. Therefore, 0.05 * M = 500, from which M is determined. Then compute the price actually paid with 20% off: 0.80 * M.

Step-by-Step Solution:
0.05 * M = 500M = 500 / 0.05 = ₹10,000Actual paid at 20% off = 0.80 * 10,000 = ₹8,000

Verification / Alternative check:
At 25% off, paid would be 0.75 * 10,000 = ₹7,500. Difference from the 20% case = 8,000 − 7,500 = ₹500, matching the statement.

Why Other Options Are Wrong:
₹10,000, ₹12,000, ₹16,000: These are not the paid price after 20% discount; ₹10,000 is the marked price, not the paid price.

Common Pitfalls:
Mistaking the ₹500 as a discount amount at 20% rather than the difference between two discounts; reporting the marked price instead of the actual paid price.

Final Answer:
₹ 8,000