Table of contents  
Clock  
Calendar  
Important Observations and Formulas of Clock  
Important Observations and Formulas for Calendars  
Sample Clock and Calendar Questions with Solution 
The number of questions related to the clock and calendar topic in competitive exams can vary greatly depending on the specific exam and its structure. Generally, these topics may constitute a small portion of the reasoning or quantitative section, with possibly 15 questions in a standard set, though this is not fixed and can change with each exam's format.
Ordinary Year: An ordinary year, which is not a leap year, consists of 365 days.
Leap Year: A leap year comprises 366 days, and it follows two conditions:
(a) Every year divisible by 4 is a leap year, except for centuries.
(b) Every 4th century is a leap year, while other centuries are not considered leap years.
When determining the day of the week for a given date, we employ the concept of 'odd days.' In a given timeframe, the days beyond complete weeks are referred to as odd days.
If the minute hand lags behind the hour hand, the angle between the two hands at M minutes past H o'clock can be calculated using the following formula:
If the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H o'clock can be determined using the following formula:
Q1: If your birthday falls on the third Monday of September 2023, on what date will your birthday fall in 2027?
Sol:
In 2023, September 1st is a Friday
The third Monday of September falls on the day after 14 days (2 weeks)
In 2027, September 1st will be a Wednesday (since the days advance by 2 days each year)
Adding 14 days (2 weeks) to Wednesday, we get Wednesday + 14 = Thursday
So, your birthday in 2027 will fall on a Thursday
Q2: Sarah set her clock to show 3 o’clock in the afternoon. How many degrees will the hour hand of the clock rotate when the clock shows 8 o’clock at night?
Sol:
From 3 o’clock in the afternoon to 8 o’clock at night is a total of 5 hours.
Since standard clock, the hour hand completes 360° in 12 hours.
So in 1 hour, it moves 360° / 12 hours = 30° per hour.
Now, for 5 hours:
Degrees rotated by the hour hand = 5 hours × 30° per hour = 150°
So, the hour hand will rotate 150° from 3 o’clock in the afternoon to 8 o’clock at night.
Q3: Determine the year in which the calendar will repeat exactly as it was in the year 2015.
Sol:
2015 is a nonleap year.
To find a year with the same calendar, we need to look for a year that is 11 years after 2015
2015 + 11 = 2026
Therefore, the calendar for the year 2026 will be the same as the calendar for the year 2015
Q4: Thomas Miller, a curious individual, approaches his mathematics teacher with a question regarding the day on which the 1st of the month will occur, given that the 9th of the month falls on the day just before Sunday.
Sol:
When the 9th of the month falls on the day preceding Sunday, we establish that the 8th of the month is a Saturday.
To determine the day when the 1st of the same month will arrive, we proceed with the following sequence:
Therefore, if the 9th of the month is positioned just before Sunday, the 1st of the same month will fall on a Friday.
Q5: A wager was made between two friends, Harry and Ronald, to determine the probability of randomly selecting a leap year that has 53 Fridays.
Sol:
2/7 in a leap year there are 366 days means 52 weeks and 2days. So already we have 52 Fridays.
Now the rest two days can be:
So, the probability of 53 Fridays = 2/7
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314 videos170 docs185 tests


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