The angle between the hour and minute hands of a clock| How to solve clock questions #logicxonomy

Here we are going to discuss some very important Clock MCQ with solutions. This chapter comes under Logical Reasoning and is frequently asked in aptitude-based exams.

The hour hand completes two 360° rotations of the clock in a day and the minute hand completes one rotation in 1 hour while the Second hand completes one rotation in 1 minute.

1 Day= 24 Hour
1 Hour= 60 Minutes
1 Minute= 60 Seconds

So, in a day there are 24×60×60=86,400 Seconds.

The circular dial of a clock is divided into 60 equal parts, called Minutes.
60 Minutes ⇒360°
1 Minute ⇒6°

In 1 hour, the hour hand covers 5 such parts which means the rotation of 5×6°=30°
So, the speed of the Hour hand= 30°/60= 0.5 Degrees/Minute

In 1 hour, the Minute hand covers 60 such parts which means the rotation of 60×6°= 360°
So, the speed of Minute hand= 360°/60= 6 Degree/Minute


When we calculate the angle between the hour hand and the minute hand of a clock, two situations are possible

1. The minute hand is behind the hour hand
2. The minute hand is ahead of the hour hand

In the given figure, the angle between the base line (0°) and the Minute hand is x° while the angle between the baseline and the Hour hand is y°.

Que: Find the angle between the hour hand and minute hand at H:M am or pm.
*(Here, H means hour and M is minute)

The rotation of Hour hand (x°)= Rotation in H hours + Rotation in M minutes
=Rotation in ‘60×H + M’ Minutes
=(60×H+M)×Speed
=(60×H+M)× 0.5 Degree/Minute
x=30×H+ 0.5×M ………..(i)

The rotation of Minute hand (y°)= Rotation in M minutes
=M×Speed
=M× 6 Degree/Minute
y=6×M ……….(ii)

Here in case:1 the angle between Hands (θ)= y-x
θ=6×M - (30×H+ 0.5×M)
θ=6×M - 30×H- 0.5×M
θ=5.5×M - 30×H
θ=11/2×M - 30×H

In case 2: the angle between Hands (θ)= x-y
θ=(30×H+ 0.5×M)- 6M
θ=30×H- 5.5×M
θ=30×H- 11/2×M
So, the general formula of angle, θ =|30H-11/2M|

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Que 1: Find the angle between Hour and Minute hand at 10:15 AM.
Solution: θ =|30H-11/2M|
Put, H=10 and M=15
=|300-82.5|
θ =217.5° or 360°-217.5°=142.5°

Que 2: Find the angle between Hour and Minute hand at 2:25 PM.
Solution: θ =|30H-11/2M|
Put, H=2 and M=25
=|60-137.5|
θ =77.5°


Top 20 Calendar MCQs (Part 2): https://youtu.be/uYNovb_XXSE

Clock MCQ with solutions (Blog): https://logicxonomy.com/clock-mcq-with-solutions/

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Home Work Problem (Will be discussed in the next Video):
A clock that moves uniformly is 6 minutes slow at 8 am on a Sunday and 6 minutes 48 seconds fast at 8 pm the following Sunday. When was it right?
(a) 20 min past 7 pm on Wednesday
(b) 35 min past 7 pm on Wednesday
(c) 50 min past 7 pm on Wednesday
(d) 24 min past 7 pm on Wednesday

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