CLOCKS PART 1

                                                       CLOCKS

                                         

Clocks” is one of the prime topics one should study to solve the questions appearing in the public sector entrance exams. It is a significant part of logical reasoning, which not only involves the in-depth logical analysis but also involves a detailed level of calculation to solve the questions in the right manner.

Every year, Clocks form an integral part of the question paper of the following list of Govt. exams that:

1. IBPS Specialist Officer
2. RRB Assistant Loco Pilot
3. Staff Selection Commission (SSC)
4. SBI PO
5. SBI Clerk
6. SBI SO
7. IBPS PO
8. IBPS Clerk

MAIN IMPORTANT LOGICS AND FORMULAS IN CLOCKS ARE:
Minute hand moves 360 degrees in 60 minutes
Hour hand moves 360 degrees in 12 hours
1 minute=6 degrees;1 hour=30(1 hr=30 degrees then 1 min=0.5 or1/2 degrees)
Relative speed of minutes(M) compared to hours(H)=5*1/2 (or)11/2 (or)5.5 degrees
Angle covered by minute hand in one minute =6degrees
Angle covered by hour hand in one minute =0.5 degrees
Angle covered by minute hand over hour hand in one minute =5.5 degrees
MAIN FORMULA1:

T = 2/11 [H*30±A]

Where:

1. T stands for the time at which the angle formed.
2. H stands for an hour, which is running.

REFLEX ANGLE: 
for reflex angle the major formula is    RA+t=360 degrees
                                                                  RA=(360-t) 
 where RA=Reflex angle ;t=angle made  
INTERCHANGE OF CLOCKS :when ever the hands of a clock interchange positions ,the sum of angles traced by minute hand and hour hand is 360 degrees (In this case the hour hand takes role as minute hand and minute hand takes role as hour hand)
  

FOR THE CLARIFICATION OF ABOVE FORMULAS AS WELL AS LOGICS YOU CAN VERIFY FROM HERE

Introduction

A Clock is a circular device provided with three hands viz. an hour hand, minute and second hand. The study of the clock is known as “horology”.

A basic structure of a clock with three hands

Structure of a Clock

A clock is composed of 360 degrees and divided into 12 equal divisions. The angle between the consecutive divisions is obtained by dividing the total angle of clock 360° by the number of divisions i.e. 12.

Twelve equal divisions of a clock

The angle between any two consecutive divisions = (360°)/12= 30°

Angle divisions of a clock

A close observation of a clock reveals that an angular space between any two consecutive divisions has further five more divisions. The area between the two divisions corresponds to a value of 5 minutes. Hence, diving the 30° by five will result in the angular value of a minute.

Angular value of a minute = (30°)/5= 6

Angular values of minutes

Angle equivalence of a minute

The table given below demonstrates the angular values of the first ten minutes:

Minute(s)	Angular values
1	6°
2	12°
3	18°
4	24°
5	30°
6	36°
7	42°
8	48°
9	54°
10	60°

Speed of the hands

A clock has three hooks and all three move at different rates. The speed of moving object depends on the distance travelled and the time taken to cover a specific range.

The speed is calculated by:

Speed = Distance/(Time taken)

The speed of a minute hand:

A minute hand travels 360° in one hour. i.e. it travels through all the 12 divisions around the clock every hour. (1 hour = 60 minutes)

Speed of a minute hand = (360°)/(60 minutes)

Speed of a minute hand = 6° per minute.

The speed of an hour hand:

An hour hand travels 30° in an hour. i.e. it covers a distance of 5 minutes (the gap between consecutive divisions) in 60 minutes.

Speed of an hour hand = (30°)/(60 minutes)

Speed of an hour hand =1/2 ° per minute.

Comparison of Speed of hands

The difference in the speed = 6°– (1/2°) = 5.5° per minute

Comparing the speed of the minute hand and an hour hand, one can conclude that the minute hand is always faster than the hour hand by 5.5° or an hour hand is always slower than the minute hand by 5.5°

Note: The evaluation of the speed of second hands is not necessary as it travels a corresponding distance of 1 second in a second.

Frequency of coincidence and collision of hands of a clock:

As we know the hands of clock moves at different speeds, they coincide and collide and also make different angle formations among themselves at various times in a day.