Clock and Calendar Tips and Tricks for Government Exams

Clock

A clock has two hands,one is the hour hand and the second is the minute hand. Both hands move around the circular dial. The hour hand is smaller than the minute hand The hour hand shows time in hours . And the minute hand shows time in minutes.

Tips & Tricks for Clocks to solve problems easily

Below are some easy tips and tricks for you on problems based on clocks which efficiently help in the competitive exam. It is a very important topic for the recruitment drive.

• Speed of the minute hand = 6° per minute.
• Speed of the hour hand = 0.5° per minute.
• Relative Speed between hour and minute hand. The relative speed of the minute hand is 6 – 0.5 dpm = 5.5 dpm. Where dpm =  dial per minute.
• Angle between Hands: To find the angle between the hour and minute hands, use the formula: |(30 x Hour – 5.5 x Minutes)|.
• Acute Angle: To find the acute angle between the hands, subtract the smaller angle from the larger angle, and take the absolute value.
• Obtuse Angle: To find the obtuse angle between the hands, subtract 360 degrees from the acute angle.
• Shortcut for 180 degrees: Whenever the minute hand points to 6 and the hour hand is at any number (1 to 11), they form a 180-degree angle.
• Shortcut for 0 degrees: Whenever the minute hand and hour hand overlap (coincide), the angle between them is 0 degrees.

Type 1:  Shortcuts on Clocks.

Example 1: What is the angle between the minute hand and the hour hand when the time is 5:30.
(a) 15 °
(b) 10°
(c) 20°
(d) None of the above
Ans: (a)
Solution: Angle covered by the hour hand (H) at 5:30:
Since the hour hand moves 30 degrees for each hour on the clock, at 5:30, it covers 5.5 hours (5 hours and 30 minutes). So, the angle covered by the hour hand is H = 5.5 x 30 = 165°
Angle covered by the minute hand (M) at 5:30:
The minute hand moves 6 degrees for each minute on the clock. At 5:30, it covers 30 minutes. So, the angle covered by the minute hand is M = 30 x 6 = 180°
Calculating the absolute difference between the two angles,
Angle between the hour and minute hands (A) = H – M = 165 – 180 = 15°

Example 2: At what time between 4 o’clock and 5 o’clock will the minute hand and the hour hand of the clock form a 90 ° angle?
Ans: Let’s assume the time is x minutes past 4 o’clock.
Angle covered by the hour hand in x minutes = 30/60 x x = x°/2.
Angle covered by the minute hand in x minutes = 360/60 x x = 6x°
For 90° angle between the hands, the difference between their angles should be 90°.
So, 6x – x/2 = 90

12x – x = 180
11x = 180
x = 180/11 ≈ 16.36 minutes
Therefore, the hands form a 90° angle approximately 16.36 minutes past 4 o’clock.

Type 2: Shortcuts to Solve Clocks

Example 1: Calculate the time between 7 and 8 o’clock when the hands of a clock are in the same straight line but are not together?
(a) 7:05(5/11 ) o’clock
(b) 7:50 (1/13) o’clock
(c) 7:20 o’clock
(d) Cannot be determined
Ans: (a)
Solution: Tip: The short formula to calculate the time when the angle is given is,
Angle = 30 (hours) – 5.5 (minutes)
Using the above formula, we get
180 = 30 (hours) – 11/2 (minutes)
180 =  30 (7) – 11/2 (minutes)
11/2 minutes = 210 - 180
Minutes = 30*2/11
= 5( 1/5)

Time = 7:05(5/11) o’clock

Example 2: What is the acute angle between the minute hand and the hour hand of a clock at 4:15?
Ans: Angle covered by the hour hand at 4:15

To find the acute angle between the hands: Acute angle = 127.5 – 90 = 37.5
Therefore, at 4:15, the acute angle between the minute hand and the hour hand is 37.5 degrees.

Calendar

Table for the month code

Tricks for the Questions When the year is 2000 or more

• First, you have to see the last three digits of the given year, if it is less than 100, then you have to add 100 in it, for example, if there 2013, then the last three digits are 013, which is less than 100 so you have to add 100 in it. like; (013+100)= 113, after that you have to divide 113 by 4, and will get a result.
• Secondly, you have to use the code of the month as given in the calendar which is given above. If there is a leap year then you have to use the code for that leap year month.
• At your third step, you have to write the date.
• Now this will be your last step, you have written all the data and add them all, after this, you will find a result.
• If you have to find the day, you have to divide it by 7, and after this, you will also get the remainder.
• Then you have to match the code of the remainder a with the given code table which is given above and you will have your answer.

Example

Example: What was the day on 26-January-2012?
(a) Friday
(b) Monday
(c) Wednesday
(d) Thursday
Ans: (d)
Solution: Now we have to see the last three digits of the year, which is 012, and add 100 to it i.e. (012 + 100 = 112), now we have to divide 112/4 = 28
Now code for January is = 6
Date is = 26
Add them all = 112 + 28 + 6 + 26 = 172
Now we have to find the day so we will divide this result 172 by 7 i.e 172/7 = 4(remainder code)
Now we have to match the remainder code 4 with code table.
4 is the code for Thursday so the answer will be Thursday.

Tricks for the questions When the year is 1999 and can be less

• In this, you have to see the last two digits of the year. For example, if there is year given 1965, then last two digits are 65, then you have to divide 65 by 4 and you will get the result for further. This is something different because here you do not need to add 100 to the last digits.
• Then the further is same as above, you have to use the month code as given in the calendar which is shown above.
• Then you have to write the date.
• Now you have to collect all the data and need to add them all. You will get a result.
• If you want to find the date you can divide this result by7, you will get a remainder.
• And as above now you have to match the code of the remainder and the code table and this way you will find the answer.

Example

Example: What was the day on 27th –November-1989?
(a) Monday
(b) Wednesday
(c) Saturday
(d) Tuesday
Ans: (d)
Solution: We have to take the year 1989, take the last two digits85, then to divide 85/4=21.25
Now we have to use the code as given above in calendar for month November is 3.
Date is 27.
Add all data = 89 + 21.25 + 3 + 27 = 140.25
Now we have to find the day so we have to divide it by 7i.e.(140.25/7 = 20.0357) we will take remainder 20.0357 as remainder code 2.
Now we have to match the remainder code with the code table in which we will see that code 2 reveals for Tuesday, so the answer is Tuesday.

Zeller’s Formula

Along with these tricks we can also use the formula of Zeller which is called Zeller’s Formula. i.e.
d = k + [(13m - 1)/5] + D + [D/4] + [C/4] - 2C mod 7

• Here d is the day of the week where we will see the day code in above given table. 
• K is the day of the month. 
• And D is the last two digits of the year
• C is the century, will take as first two digits of the year. 
• The [ ] brackets reveals to the high integer function. 
• Which is the largest integer less than and equal to the number inside. 
• M = month, but we will start the year with the month March = 1, so January and February will the 11th and 12th month of the last year.

Example

Example: What was the day on 7- December-1941?
(As I know it was Sunday, but here I will do through this formula)
Ans: d = 7 + [(13 * 10 - 1)/5] + 41 + [41/4] + [19/4] - 2 * 19 mod 7
= 7 + [25.8] + 41 + [10.25] + [4.75] - 38 mod 7
= 7 + 25 + 41 + 10 + 4 - 38 mod 7
= 49 mod 7
= 0 mode 7
So here we got the 0, which reveals I table code as Sunday, so the answer is Sunday. This formula works only for the Gregorian calendar.