Clocks is an important chapter for reasoning ability. We can see few questions from this chapter in various bank exams. This post is a part of Quantitative Aptitude Preparation series.
Basic Principles
1) How many degrees a hand covers in an hour
In one hour, hour hand covers = 360/12 = 30°
In one minutes, minutes and covers = 360/60 = 6°
2) It is 2 pm now. In how much time minute and hour hands meet each other again ?
Simply minutes hand run faster than hour hand. At 3 pm, minutes hand need to cover minutes to reach hours hand but while minutes hand reach hour hand, hour hand will cover "some distance".
Now how to calculate "some distance".
Simply multiply 10 minutes with 60/55.
10 x 60/55 = 10.90 or 10 minutes 54 seconds
Solution - Best way to get solution is by finding angle of each hand from 12 noon.
Angle of minutes hand from 12 noon = 30 x 6 = 180°
Angle of hour hand from 12 noon = (3 x 30) + (0.5 x 30) = 105°
By deducting bigger angle from smaller angle, answer is = 180° - 105°
Question - At what time hour hand and minutes hand meet each other between 3 pm and 4 pm clock ?
Solution - Minutes hand will reach 3 pm within 15 minutes but hour hand will also move during this time.
Now again you need to calculate that "some distance".
Simply multiply 15 minutes with 60/55.
15 x 60/55 = 180/11 minutes past 3 pm
In one minutes, minutes and covers = 360/60 = 6°
2) It is 2 pm now. In how much time minute and hour hands meet each other again ?
Simply minutes hand run faster than hour hand. At 3 pm, minutes hand need to cover minutes to reach hours hand but while minutes hand reach hour hand, hour hand will cover "some distance".
Now how to calculate "some distance".
Simply multiply 10 minutes with 60/55.
10 x 60/55 = 10.90 or 10 minutes 54 seconds
Examples
Question - At 3:30, hour and minute hand makes an angle of ?Solution - Best way to get solution is by finding angle of each hand from 12 noon.
Angle of minutes hand from 12 noon = 30 x 6 = 180°
Angle of hour hand from 12 noon = (3 x 30) + (0.5 x 30) = 105°
By deducting bigger angle from smaller angle, answer is = 180° - 105°
Question - At what time hour hand and minutes hand meet each other between 3 pm and 4 pm clock ?
Solution - Minutes hand will reach 3 pm within 15 minutes but hour hand will also move during this time.
Now again you need to calculate that "some distance".
Simply multiply 15 minutes with 60/55.
15 x 60/55 = 180/11 minutes past 3 pm
