A clock is a tool used to show and keep time. It is an electronic device that produces hours, minutes, and seconds. Different types of questions are asked in the reasoning section of the clock, the angle between the hands of the clock, the position of the hands of the clock, and so on.

**1.** Minute hand and hour hand coincides once in every hour. They coincide 11 times in 12 hours & 22 times in 24 hours. They don't coincide between 12 & 1O'Clock.

**2.** Minute hand & hour hand are opposite once in every hour. Then the two hands are opposite in direction, distance between them is of 30 minutes. They make an angle of 180° with each other. They do it 11 times in 12 hours & 22 times in 24 hours. It doesn't happen between 6 to 7 O'clock.

**3.** Both hands (Minute & hour) are perpendicular twice in every hour. They make an angle of 90° 22 times in 12 hours and 44 times in 24 hours.

**4.** In One Minute, hour hand moves 1/2° & Minute hand moves 6°. In One hour, hour hand moves 30° & minute hand moves 360°.

**5.** In an hour, minute hand moves 55 minutes ahead of hour hand.

To find the time of Coincidence of two hands of the clock. We multiply 5 x 5/11 with the time.

1. At what time between 3 & 4 will the two hands coincide ?

Sol. 60/11 = 3 & 3 x 5x 5/11 = 15 x 5/11 = 16 x 4/11

= 3 & 16 x 4/11 minutes

1. At what time between 2 & 3 will the two hands be opposite ?

Sol. At 2 o'clock the distance between the two hands is 10 minutes. When they are at 30 minutes distance, they are opposite to each other. The time taken (30 + 10 ) = 40 minutes.

minute hand is 55 minutes ahead of hour hand in 60 minutes.

_____________ 1 minute __________________ 60/55

______________ 40 minutes ________________60 x 40/55= 2 & 43 x 7/55 minute

1 & 2 |
2 & 3 |
3 & 4 |
4 & 5 |
5 & 6 |
6 & 7 |
7 & 8 |
8 & 9 |
9 & 10 |
10 &11 |
11 & 12 |
12 & 1 |

1 & 38 2/11 |
2 & 43 7/11 |
3 & 49 1/11 |
4 & 54 6/11 |
6 |
6 |
7 & 5 5/11 |
8 & 10 10/11 |
9 & 16 4/11 |
10 & 21 9/11 |
11 & 27 3/11 |
12 & 32 8/11 |

Time is multiplied by 5 x 5/11 (Time ± 3)