2024 is a leap year (as February has 29 days). Leap years occur in the years that are multiples of 4, except for those years that are divisible by 100 but not 400.

(i) From the year you were born till now, which years were leap years?

(ii) From the year 2024 till 2099, how many leap years are there?

(i) This depends on the student's year of birth. The student should list all years which are multiples of 4 (and not exceptions) from their birth year up to the present year.

For example, if the student was born in 2014 and the present year is 2026, the leap years are: 2016, 2020, 2024.

Hence, list the multiples of 4 between your birth year and the present year, excluding any year divisible by 100 but not by 400.

(ii) From 2024 till 2099 (both inclusive):

Multiples of 4 from 2024 to 2096:

2024, 2028, 2032, …, 2096.

This forms an arithmetic sequence with first term 2024, common difference 4 and last term 2096.

Number of terms = $\dfrac{2096 - 2024}{4} + 1 = \dfrac{72}{4} + 1 = 18 + 1 = 19$.

We must check exceptions: years divisible by 100 but not 400 are not leap years. The only century year in this range is 2100, but 2100 > 2099, so it's not in our range. There are no exceptions in 2024–2099.

Hence, there are 19 leap years from 2024 till 2099.