A person had some rupees which is a power of 5. He gave a part of it to his friend which is also a power of 5. He was left with ₹ 500. How much did money he have?

Let the money he have be Rs 5^x and that he gave to his friend be Rs 5^y, such that x>y.

According to the question,

5^x - 5^y = 500

We can see from the equation that 5^x> 500 because 500 is the money that he is left with.

So 5^x = 625

⇒ x = 4

Then 625 - 5^y = 500

⇒5^y = 125

⇒ y = 3

So, the money he had = Rs 625 and that he gave to his friend = Rs 125