How many times does the 29th day of the month occur in 400 consecutive years?

Correct option is C

Given:

29th day of the month occur in 400 consecutive years.

Logic:

A month will have the 29th day if it has at least 29 days. This excludes February in non-leap years, as it only has 28 days

In 400 consecutive years:
A leap year occurs every 4 years, but years divisible by 100 are not leap years unless they are also divisible by 400.
Thus, in 400 years:.

Regular Leap Years: $$\frac{400}{4} = 100$$​
Excluded Century Years: $$\frac{400}{100} = 4$$​ (but divisible by 400 are included)
Final count of leap years: 100 - 4 + 1(400th year) = 97

Months other than February always have at least 29 days.
February has 29 days only in leap years.

In 400 years, there are 12 months per year:
12 × 400 = 4800 months.

Exclude February in non-leap years (it won’t have the 29th day):
Non-leap years = 400 − 97 = 303.
February in non-leap years = 303 × 1 = 303 months without the 29th day.

Total months with the 29th day: 4800 − 303 = 4497.

So, the 29th day of the month occurs 4497 times in 400 consecutive years.

Thus, the correct answer is (c).