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 1-5 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 non-leap 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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