Question

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 Rs.$500$. How much money did he have?

Answer 1

Suppose, a person has $5^x$ rupees.

Suppose, he gave $5^y$ rupees to his friend.

$⟹5^x-5^y=500$ ..........$\left(i\right)$ [Given]

$⟹5^x=500+5^y$

If $y=1,5^x=505$ which is not a power of $5$. So, it is not possible

If $y=2,5^x=525$ which is not a power of $5$. So, it is not possible

If $y=3,5^x=625=5^4$ which is a power of $5$.

Hence, the person have $625$ rupees.