CLOCKS

Simple Problems Shortcuts in clocks :

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.