Mr X bought a music system with 20% discount on the labelled price. Had he bought it with 25% discount, he would have saved ₹ 500. At what price did he buy the music system?

Let the actual price of music system = ₹ P
The cost of music system to Mr. P after 20% discount= (80/100) x P = 4P/5
Cost of music system to Mr P after 25% discount = (75/100) x P = 3P/4
Then according to the question,
4P/5 - 3P/4 = 500
⇒ (16P - 15P)/20 = 500
∴ P = 20 x 500 = 10000
∴ Cost of music system at 20% discount = (80 x 10000)/100 = ₹8000