Page 239 - Services Selection Board (SSB) Interviews

Chapter
Chapter
17 Clocks

Section Level No. of Questions

Concept Applicator Very Easy 10
Concept Builder Easy 15

SALIENT FEATURES OF A CLOCK

(i) A clock has 12 divisions (equally spaced) hence each division is 360/12 = 30°.
(ii) A clock has two hands, smaller hand is called short hand or hour hand. While larger hand is called long hand or
minute hand.
(iii) Angle traced by minute hand in 60 minutes are 360 that means speed of minute hand is 6°/min.

(iv) Angle traced by hour hand in 12 hours = 360° that means speed of minute hand is ½ °/min.
(v) Relative speed between Minute hand and hour hand is (6 – ½) = 11/2 °/min
(vi) Both hands of clock coincides in one hour
(vii) In each 60 minutes, the minute hand gains 55 minutes on the hour hand
(viii) When both the hands are at right angle, they are 15 minutes space apart

(ix) Both hands are in straight line when they are opposite to each other or coincident to each other.
(x) Clock hands coincide 11 times in every 12 hours, as they coincides only one time between 11 and 1, at 12 o’clock.
Hence, Both hands coincides 22 times in 24 hours or in a day.
(xi) In 12 hours both hands are in straight line (either coincides or in opposite direction) 22 times. Hence in 24 hours
both hands are in straight line 44 times.

(xii) In 12 hours both hands are at right angled 22 times and 44 times in a day (as in the case of coincide)
(xiii) In 12 hours both hands are in opposite direction 11 times, between 5 to 7, they are opposite at 6 o’clock only.
Hence in a day they are 22 times in opposite directions.
o
Since relative speed between minute hand and hour hand is 11/2 per min or in other words minute hand will travel
o
11/2 more than hour hand. Lets these two hands are together, they will again be together when minute hand will travel
o
360 more than hour hand i.e after (360)/(11/2) = 720/11 or after 65 5/11 minute.
So we can conclude that after every 65 5/11 minute these two hands will be together.

In a day i.e 12 hours or 12 × 60 minute (12 × 60)/(720/11) = 11 times these two hands will be together.
Angle between two hands: Let we have to find angle between minute hand and hour hand at ‘P hours and Q
minutes’. Consider from 12:00 when these two hands are together. Total time passed since 12:00 to P hour Q minute
is (60P + Q) Minute. In this time angle moved by Hour hand is (60P +Q)/2 degrees.