The calendar of the leap year 2024 (same sequence of days and dates) can be reused without any change in which of the following future years?

Introduction: This question asks when the calendar for 2024 can be used again unchanged. Since 2024 is a leap year, the future year must also be a leap year and must start on the same day of the week. Calendar repetition questions commonly appear in aptitude exams and rely on understanding leap-year patterns and weekday shifts.

Given Data / Assumptions: Base year: 2024. 2024 is a leap year (divisible by 4 and not a century year). We need the earliest future year among the options where the day-date pattern is identical.

Concept / Approach: In the Gregorian calendar, each non-leap year shifts the starting weekday of the next year by 1 day, while each leap year shifts it by 2 days. For a calendar to repeat, the total shift in weekdays from the base year must be a multiple of 7, and the candidate year must have the same leap/non-leap status as the base year. Leap year calendars often repeat after 28 years, but depending on the century pattern, sometimes other intervals appear; here, we primarily look at the standard 28-year cycle.

Step-by-Step Solution: Step 1: Check that 2024 is a leap year. 2024 ÷ 4 = 506 with no remainder, and it is not divisible by 100, so it is a leap year. Step 2: Consider the standard repetition interval. Leap year calendars commonly repeat every 28 years because of the 7-day week and the 4-year leap cycle. Adding 28 years to 2024 gives 2024 + 28 = 2052. Step 3: Check that 2052 is a leap year. 2052 ÷ 4 is an integer and it is not a century year, so it is also a leap year. Step 4: Conclude that 2024 and 2052 share the same day-date arrangement. The weekday of 1 January and all other dates aligns exactly when the 28-year cycle condition is met and both years are leap years.

Verification / Alternative check: If we examine an actual calendar for 2024 and 2052, we would see that the weekdays for all dates match exactly (for example, 1 January is on the same weekday and 29 February exists in both years). This empirical check supports our theoretical reasoning.

Why Other Options Are Wrong: 2030, 2036, 2048, 2060: Even if some of these years are leap years, their starting weekdays do not line up correctly with that of 2024, so the full calendar is not identical.

Common Pitfalls: A frequent mistake is to pick the next leap year (such as 2028 or 2032) without verifying the weekday alignment. Another is to forget that non-leap and leap years behave differently, so they cannot share identical calendars.

Final Answer: The calendar of 2024 can be used again in 2052.