Clock

Clock is a topic where questions are asked about finding the angle between the hour and minute hands at a given time, finding the time when the hands are at a certain angle, or finding the number of times the hands overlap or are at right angles. It is a scoring topic that uses simple formulas.

Basic Facts About a Clock:

• A clock has 12 hours and is divided into 60 minutes
• The minute hand completes 1 full rotation (360°) in 60 minutes
• The hour hand completes 1 full rotation (360°) in 12 hours
• Speed of minute hand = 360° ÷ 60 = 6° per minute
• Speed of hour hand = 360° ÷ 720 = 0.5° per minute
• Relative speed of minute hand over hour hand = 6 - 0.5 = 5.5° per minute

Types of Clock Questions in SSC CGL:

Type 1 - Finding the Angle Between Hands

Formula: Angle = |11M/2 - 30H|

Where:

• M = Minutes
• H = Hours
• | | means take the absolute value (always positive)
• If angle > 180°, subtract from 360° to get the smaller angle

Example: 

Find the angle between hands at 3:30

H = 3, M = 30 

Angle = |11×30/2 - 30×3| 

= |165 - 90| = 75°

Answer: 75°

Type 2 - Finding Time When Angle is Given The angle between hands is given and you have to find the time.

Example: 

At what time between 4 and 5 o'clock will the hands of the clock be at right angles (90°)?

Solution: 

Use formula: M = 2(30H ± θ) / 11

For right angle (θ = 90°) and H = 4: 

M = 2(30×4 + 90) / 11 = 2(120+90)/11 = 2×210/11 = 420/11 = 38 2/11 minutes 

So time = 4 hours 38 2/11 minutes

Also: M = 2(30×4 - 90) / 11 = 2(120-90)/11 = 2×30/11 = 60/11 = 5 5/11 minutes 

So time = 4 hours 5 5/11 minutes

Answer: 4:05 5/11 and 4:38 2/11

Type 3 - Hands Overlap (Coincide) Both hands point in the same direction (0° angle between them).

Formula: M = 60H/11

Example: 

After 3 o'clock, when do hands overlap? 

M = 60×3/11 = 180/11 = 16 4/11 minutes 

So hands overlap at 3:16 4/11

Key Facts about Overlapping:

• Hands overlap 22 times in 24 hours
• Hands overlap 11 times in 12 hours
• Hands overlap approximately every 65 5/11 minutes

Type 4 - Hands Opposite (180° apart) Both hands point in opposite directions.

Formula: M = 2(30H + 180) / 11

Example: 

After 6 o'clock, when are hands opposite? 

M = 2(30×6 + 180)/11 = 2(180+180)/11 = 2×360/11 = 720/11 = 65 5/11 minutes 

But 65 5/11 > 60 so this means it happens at 7:05 5/11

Key Facts about Opposite Hands:

• Hands are opposite 22 times in 24 hours
• Hands are opposite 11 times in 12 hours

Type 5 - Faulty Clock A clock gains or loses time. Find the actual time.

Example: 

A clock gains 5 minutes every hour. If it shows 3:00 PM now, what is the actual time?

Logic: 

For every 65 minutes shown by faulty clock = 60 minutes actual time 

Find actual time based on how many minutes gained.

How to Solve Clock Questions:

Step 1 - Identify what is asked - angle, time or overlap. 

Step 2 - Write down H (hours) and M (minutes) from the given time. 

Step 3 - Apply the correct formula. 

Step 4 - Calculate carefully - these questions involve fractions. 

Step 5 - If angle > 180°, subtract from 360° to get reflex angle.

Important Formulas - Must Memorize:

Quick Tricks:

Trick 1 - At every exact hour H:00, the minute hand is at 12 and hour hand is at H×30°.

Trick 2 - The angle between hands increases by 5.5° every minute.

Trick 3 - Hands overlap 11 times every 12 hours (not 12 times - they do not overlap separately at 12).

Trick 4 - For mirror image time formula: Mirror time = 11:60 - Given time (same as what we learned in Mirror chapter).

Trick 5 - Always verify your answer by checking if the calculated angle matches the expected angle.

Important Tips:

• Memorize the main formula: Angle = |11M/2 - 30H|
• Always use fractions when required - do not round off
• 1 to 2 questions come from this topic in SSC CGL every year
• Practice at least 10 clock questions daily
• This topic and Calendar together are solved fastest in the reasoning section