8 CLOCKS
In a clock the most important hands are the minutes hand and the hours hand. Whatever may be the shape
ofthe dial they move in a circular track.
The total angle of 360 degrees in a watch is divided into I sectors, one for each hour.
So one hour sector = 360/ 12=30 degrees.
For every one hour (60 min),
The minutes hand moves through 360 deg.
The hours hand moves through 30 deg.
So for every minute,
The minutes hand moves through 6 deg
The hours hand moves through 0.5 deg.
They move in same direction. So their relative displacement for every minute is 5.5 deg.
This 5.5 deg movement constitutes the movements ofboth the hands.
So for every minute both the hands give a displacement of5.5 deg.
Note:
1. Between every two hours i.e., between 1 and 2, 2 and 3 and so on the hands ofthe clock coincide with each
other for one time except between 11, 12 and 12, 1.
Ina day they coincide for 22 times.
Between every two hours they are perpendicular to each other two times except between 2, 3 and 3, 4 and
2
8,9 and 9, 10.
Ina day they will be perpendicular for 44 times.
3. Between every two hours they will be opposite to each other one time except between 5, 6 and 6,7.
Inaday they will be opposite for 22 times.
Examples:
1. At what time between 5 and 6 will the hands ofthe clock coincide?
Soln At S
the angle between the hands is 150 deg.
, lo coincide, they collectively have to travel this distance. Every minute they travel 5.5 deg.
So no. ofminutes required to coincide =1 50/5.5=300/11 =27 3/11 min.
2. At what time between 6 and 7 will the hands be perpendicular?
Soln: At 6 the angle between the hands is 180 deg.
lo form 90 deg they have to cover 90 deg (out of 180 if90 is covered 90 will remain)
16 4/1| min.
So no.
of minutesrequired =90/5.5 180/11
=
But they will be perpendicular for two times. The second one will happen after the minutes hand crosses th
hours hand and then for 90 deg.
So it has to travel 180+90 270 deg.
So time =270/5.5 540/11 = 49 1/11 min.
3. What is the angle between the hands ofthe clock at 3.45?
Soln: At 3, the angle between the hands -A=90deg.
In 45 min the hands will move angle ofB = 45 X 5.5 deg (since 5.5 deg for I min)
B 247.5 deg.
Required angle =A~B=157.5 deg.
4. What is the angle between the hands at 4.40?
Soln: At 4 the anglebetweenthe hands, A= 120 deg.
In 40 min, B= 40 X 5.5 220 deg.
The required angle = A ~ B = 100 deg.
A clock loses 5 min for every hour and another
gains 5 min for every hour. If they are set correct a l0 am
on Monday then when will they be 12 hrs apart?
Soln: For every hour watch A loSes 5 min and watch B gains 5 min
So for every hour they will differ by 10 min.
12 hrs (720 min) diflerence between them the time
required =720/10=72 hrs
So they will be 12 hrs apart ater 5 days i.e., at 10 am on
Thursday.
In a clock the most important hands are the minutes hand and the hours hand. Whatever may be the shape
ofthe dial they move in a circular track.
The total angle of 360 degrees in a watch is divided into I sectors, one for each hour.
So one hour sector = 360/ 12=30 degrees.
For every one hour (60 min),
The minutes hand moves through 360 deg.
The hours hand moves through 30 deg.
So for every minute,
The minutes hand moves through 6 deg
The hours hand moves through 0.5 deg.
They move in same direction. So their relative displacement for every minute is 5.5 deg.
This 5.5 deg movement constitutes the movements ofboth the hands.
So for every minute both the hands give a displacement of5.5 deg.
Note:
1. Between every two hours i.e., between 1 and 2, 2 and 3 and so on the hands ofthe clock coincide with each
other for one time except between 11, 12 and 12, 1.
Ina day they coincide for 22 times.
Between every two hours they are perpendicular to each other two times except between 2, 3 and 3, 4 and
2
8,9 and 9, 10.
Ina day they will be perpendicular for 44 times.
3. Between every two hours they will be opposite to each other one time except between 5, 6 and 6,7.
Inaday they will be opposite for 22 times.
Examples:
1. At what time between 5 and 6 will the hands ofthe clock coincide?
Soln At S
the angle between the hands is 150 deg.
, lo coincide, they collectively have to travel this distance. Every minute they travel 5.5 deg.
So no. ofminutes required to coincide =1 50/5.5=300/11 =27 3/11 min.
2. At what time between 6 and 7 will the hands be perpendicular?
Soln: At 6 the angle between the hands is 180 deg.
lo form 90 deg they have to cover 90 deg (out of 180 if90 is covered 90 will remain)
16 4/1| min.
So no.
of minutesrequired =90/5.5 180/11
=
But they will be perpendicular for two times. The second one will happen after the minutes hand crosses th
hours hand and then for 90 deg.
So it has to travel 180+90 270 deg.
So time =270/5.5 540/11 = 49 1/11 min.
3. What is the angle between the hands ofthe clock at 3.45?
Soln: At 3, the angle between the hands -A=90deg.
In 45 min the hands will move angle ofB = 45 X 5.5 deg (since 5.5 deg for I min)
B 247.5 deg.
Required angle =A~B=157.5 deg.
4. What is the angle between the hands at 4.40?
Soln: At 4 the anglebetweenthe hands, A= 120 deg.
In 40 min, B= 40 X 5.5 220 deg.
The required angle = A ~ B = 100 deg.
A clock loses 5 min for every hour and another
gains 5 min for every hour. If they are set correct a l0 am
on Monday then when will they be 12 hrs apart?
Soln: For every hour watch A loSes 5 min and watch B gains 5 min
So for every hour they will differ by 10 min.
12 hrs (720 min) diflerence between them the time
required =720/10=72 hrs
So they will be 12 hrs apart ater 5 days i.e., at 10 am on
Thursday.
