Clock & Calendar for the Assam Police Constable (AB & UB) Exam
Clock and Calendar is a reasoning topic of the SLPRB Assam Police Constable (AB & UB) examination in which the candidate must find the angle between the hands of a clock, the time at which the hands are together or opposite, or the day of the week on a given date. The topic needs no general knowledge and only simple arithmetic, and it rests on two or three fixed facts. A candidate who remembers the basic values almost never makes a mistake. This page explains the rules, the worked examples, the shortcuts and the traps that cost marks. The material follows the standard reasoning reference books used for Assam recruitment examinations and is reviewed before it is published.
What the Topic Means
In clock problems a circular dial is divided into twelve hours and sixty minutes, and the hour hand and the minute hand move at fixed speeds. The candidate must find the angle between the two hands at a given time, the time when the hands are together, opposite or at right angles, or the number of times the hands coincide in a day. In calendar problems the candidate must find the day of the week for a given date, using the number of odd days in a month, a year or a century.
The Basic Facts to Remember
- The minute hand moves six degrees a minute and the hour hand moves half a degree a minute.
- The minute hand gains eleven half-degrees over the hour hand every minute, so the gap changes by five and a half degrees a minute.
- At a given hour, the angle between the hands is thirty times the hour minus five and a half times the minutes.
- The hands coincide eleven times in twelve hours and twenty-two times in a day.
- Odd days: an ordinary year has one odd day and a leap year has two odd days.
A Step by Step Method
- Write the given time in hours and minutes.
- Use the angle formula, take the modulus, and if the answer is more than 180 degrees, subtract it from 360.
- For coincidence questions set the angle to zero; for opposite set it to 180; for right angles set it to 90.
- For calendar questions count the odd days from a known reference date, such as 1 January 1, and take the remainder by seven.
- Check the answer against the dial or a known day.
Worked Examples
Example one: at 3 o'clock the angle is 3 times 30, that is 90 degrees. Example two: at 3:30 the angle is 3 times 30 minus 5.5 times 30, whose modulus is 75 degrees. Example three: the hands are together at 12:00 and then every hour and five and a half minutes. Example four: if 1 January 2024 is a Monday, then 1 January 2025 is a Tuesday, because 2024 is a leap year and has two odd days.
How This Topic Appears in the Examination
The topic usually appears as two to four objective questions of one mark each. The common forms are to find the angle between the hands, the time when the hands are together or opposite, the number of coincidences in a day, and the day of the week for a given date. The questions are quick because they use one formula or one count each.
Shortcuts and Speed Methods
- Remember the angle formula as thirty times the hour minus five and a half times the minutes.
- For coincidence and opposite questions use the standard times, such as the hands being opposite at 6 o'clock.
- Count odd days quickly by noting that a leap year adds two and an ordinary year adds one.
- In a day the hands coincide twenty-two times.
- Check the answer by drawing a small dial once.
Common Mistakes to Avoid
- Forgetting to take the modulus of the angle or to reduce an answer above 180 degrees.
- Mixing up the speed of the hour hand and the minute hand.
- Counting a leap year as one odd day instead of two.
- Counting one hand's movement as the whole angle.
- Applying the angle formula for a calendar question.
Preparation Plan
- Learn the two speeds and the angle formula by heart.
- Practise twenty clock questions a day with a small dial each time.
- Solve coincidence, opposite and right-angle questions separately.
- Practise the odd-days method for at least ten years.
- Revise the basic values once a week.
More Practice Questions
- At 4 o'clock the angle between the hands is 120 degrees.
- At 6 o'clock the hands are exactly opposite, that is 180 degrees.
- The hands coincide twenty-two times in a day.
- If today is Sunday, after 60 days, which has four odd days, the day will be Thursday.
- In a common year there is one odd day and in a leap year two.
Quick Revision Checklist
- Minute hand six degrees a minute, hour hand half a degree a minute.
- Angle is thirty times the hour minus five and a half times the minutes.
- Hands coincide eleven times in twelve hours and twenty-two in a day.
- Ordinary year one odd day, leap year two odd days.
- Always draw the dial and check by counting.
Frequently Asked Questions
What is the clock and calendar topic?
It is a reasoning topic in which the candidate finds the angle between the hands of a clock, the time when the hands are together or opposite, or the day of the week for a given date.
What is the angle formula for a clock?
The angle is thirty times the hour minus five and a half times the minutes, and the modulus is taken so that the answer lies between zero and 180 degrees.
How many times do the hands coincide in a day?
The hands coincide eleven times in twelve hours and so twenty-two times in a day, because the minute hand gains a full round over the hour hand each time.
How do I find the day of the week for a date?
Count the odd days from a known reference date, remembering that an ordinary year contributes one odd day and a leap year two, and then take the remainder by seven.
Is clock and calendar scoring in Assam Police?
Yes. Each question uses one formula or one count and can be solved in a few seconds, so it is a good place to gain sure marks in the reasoning paper.