The difference between two numbers is 5 and the difference between their squares is 65. What is the larger number?

Question: The difference between two numbers is 5 and the difference between their squares is 65. What is the larger number?

Solution:
Let the larger number is = n
Then, the other number is = n - 5

ATQ,
n² - (n - 5)² = 65
⇒ n² - n² + 10n - 25 = 65
⇒ 10n = 65 + 25
⇒ 10n = 90
⇒ n = 90/10
∴ n = 9

So, the larger number is 9.