Clock Tricks

In every hour:

(a) Both the hands coincide once.

(b) When the hands opposite directions, they are 30 minutes spaces apart.

(c) When the two hands are at a right angle, they are 15 minutes spaces apart.

• The minute needle makes an angle of 6 degrees in 1 minute.
• The hourly needle makes an angle of 1/2 degree in 1 minute.
• When the hands are coincident, the angle between them is 0°.
• When the hands point in opposite directions, the angle between them is 180°.
• The minute hand moves 12 times as fast as the hour hand.

Clock Reasoning Tricks

The minute hand of a clock overtakes the hour hand at intervals of M mins of correct time. The clock gains or losses in a day by:

Example: The minute hand of a clock overtakes the hour hand at intervals of 65 mins. How much a day does the clock gain or lose?

Solution: Here, M= 65

The angle between the hands of a clock

(a) When the minute hand is behind the hour hand, the angle between the two hands at M mins past H O’clock

(b) When the minute hand is ahead of the hour hand, the angle between the two hands at M mins past H O’clock

Example: What is the angle between the two hands of a clock when the time is 15 minutes past 4 O’clock ?

Solution: Here, H = 4, M= 15

= 30 + 7.5 degrees

= 37.5°

Example: Find the angle between the hour hand and the minute hand of a clock when it is 38 minutes past 7 pm ? 

Solution: Here, H = 7, M= 38

= 30  – 19 degrees

= 18 – 19 degrees = 1°

The two hands of the clock will be at right angle between H and (H + 1) O’clock at

Case 1: When the minute hand is 15 mins spaces behind the hour hand, to be in this position, the minute hand will have to gain (5H – 15) mins spaces over the hour hand.

Case 2: When the minute hand is 15 mins spaces ahead of the hour hand, to be in this position, the minute hand will have to gain (5H + 15) mins spaces over the how hand.

Example: At what time between 5 and 6 O’clock will the hands of a clock be at right angle ?

Solution: Here, H = 5

The two hands of the clock will be in the same straight line but not together between H and (H + 1) O’clock at

Example: Find at what time between 2 and 3 O’clock will the hands of a clock be in the same straight line but not together.

Solution: Here, 2 < 6

So, the hands will be in the same straight line but not together

Example: At what time between 7 and 8 O’clock will the hands of a clock be in same straight line but not together ?

Solution: 

So, the hands will be in the same straight line but not together

The two hands of the clock will be together between H and (H + 1) O’clock at

Example: At what time between 9 and 10 O’clock will the hands of a watch be together?

Solution: Here, H = 9

Example: At what time between 3 and 4 O’ Clock will the two hands coincide ?

Solution: Here, H = 3

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