business mathematics

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