General Concepts:
The face or dial of a watch is a circle whose circumference is divided into 60 equal parts,called minute spaces.
A clock has two hands, the Smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
Important points:
a) In every 60 minutes, the minute hand gains 55 minutes on the hour hand
b)In every hour, both the hands coincide once ,i.e 0 degrees.
c)the hands are in the same straight line when they are coincident or opposite to each other. i.e 0 degrees or 180 degrees.
d)when the two hands are at right angles, they are 15 minute spaces apart,i.e 90 degrees.
e)when the hands are in the opposite directions,they are 30 minute spaces apart,i.e 180 degrees.
f)Angle traced by hour hand in 12hrs = 360 degrees.
g)Angle traced by minute hand in 60 min = 360 degrees. If a watch or a clock indicated 8.15,when the correct time is 8, it is said to be 15 minutes too fast. On the other hand, if it indicates 7.45, when the correct time is 8,it is said to be 15 minutes slow.
h)60 min --> 360 degrees
1 min --> 60
i)the hands of a clock coincide in a day or 24 hours is 22 times, in 12hours 11minutes.
j)the hands of clock are straight in a day is 44 times .
k)the hands of a clock at right angle in a day is 44 times .
l)the hands of a clock in straight line but opposite in direction is 22 times per day
Simple Problems:
Type1:
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
solution : In this type of problems the formulae is as follows
30*[hrs-(min/5)]+(min/2)
In the above problem the given data is time is 3.25. that is
applied in the
formulae
30*[3-(25/5)]+(25/2)30*(15-25)/5+25/2
= 30*(-10/5)+25/2
= -300/5+25/2
= -600+(25/2)=-475/10=-47.5
i.e 47 1/20
therefore the required angle is 47 1/20.
Note:The -sign must be neglected.
Another shortcut for type1 is :
The formulae is
6*x-(hrs*60+X)/2
Here x is the given minutes,
so in the given problem the minutes is 25 minutes,
that is applied in the given formulae
6*25-(3*60+25)/2
150-205/2
(300-205)/2=95/2
=47 1/20.
therefore the required angle is 47 1/20.
Type2:
At what time between 2 and 3 o' clock will be the hands of a clock be together?
Solution : In this type of problems the formulae is
5*x*(12/11)
Here x is replaced by the first interval of given time.
here i.e 2. In the above problem the given data is between
2 and 3 o' clock
5*2*12/11 =10*12/11=120/11=10 10/11min.
Therefore the hands will coincide at 10 10/11 min.past2.
Another shortcut for type2 is:
Here the clocks be together but not opposite
to each other so the angle is 0 degrees. so the formulae is
6*x-(2*60+x)/2=06*x-(120+x)/2=012x-120-x=0
11x=120
x=120/11=10 10/11
therefore the hands will be coincide at 10 10/11 min.past2.
The face or dial of a watch is a circle whose circumference is divided into 60 equal parts,called minute spaces.
A clock has two hands, the Smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
Important points:
a) In every 60 minutes, the minute hand gains 55 minutes on the hour hand
b)In every hour, both the hands coincide once ,i.e 0 degrees.
c)the hands are in the same straight line when they are coincident or opposite to each other. i.e 0 degrees or 180 degrees.
d)when the two hands are at right angles, they are 15 minute spaces apart,i.e 90 degrees.
e)when the hands are in the opposite directions,they are 30 minute spaces apart,i.e 180 degrees.
f)Angle traced by hour hand in 12hrs = 360 degrees.
g)Angle traced by minute hand in 60 min = 360 degrees. If a watch or a clock indicated 8.15,when the correct time is 8, it is said to be 15 minutes too fast. On the other hand, if it indicates 7.45, when the correct time is 8,it is said to be 15 minutes slow.
h)60 min --> 360 degrees
1 min --> 60
i)the hands of a clock coincide in a day or 24 hours is 22 times, in 12hours 11minutes.
j)the hands of clock are straight in a day is 44 times .
k)the hands of a clock at right angle in a day is 44 times .
l)the hands of a clock in straight line but opposite in direction is 22 times per day
Simple Problems:
Type1:
Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
solution : In this type of problems the formulae is as follows
30*[hrs-(min/5)]+(min/2)
In the above problem the given data is time is 3.25. that is
applied in the
formulae
30*[3-(25/5)]+(25/2)30*(15-25)/5+25/2
= 30*(-10/5)+25/2
= -300/5+25/2
= -600+(25/2)=-475/10=-47.5
i.e 47 1/20
therefore the required angle is 47 1/20.
Note:The -sign must be neglected.
Another shortcut for type1 is :
The formulae is
6*x-(hrs*60+X)/2
Here x is the given minutes,
so in the given problem the minutes is 25 minutes,
that is applied in the given formulae
6*25-(3*60+25)/2
150-205/2
(300-205)/2=95/2
=47 1/20.
therefore the required angle is 47 1/20.
Type2:
At what time between 2 and 3 o' clock will be the hands of a clock be together?
Solution : In this type of problems the formulae is
5*x*(12/11)
Here x is replaced by the first interval of given time.
here i.e 2. In the above problem the given data is between
2 and 3 o' clock
5*2*12/11 =10*12/11=120/11=10 10/11min.
Therefore the hands will coincide at 10 10/11 min.past2.
Another shortcut for type2 is:
Here the clocks be together but not opposite
to each other so the angle is 0 degrees. so the formulae is
6*x-(2*60+x)/2=06*x-(120+x)/2=012x-120-x=0
11x=120
x=120/11=10 10/11
therefore the hands will be coincide at 10 10/11 min.past2.
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