IMPORTANT FORMULAE RELATED TO
CLOCK
Minute Spaces:
The face or dial of watch is a circle whose circumference is divided
into 60 equal parts, called minute spaces.
Hour Hand and Minute Hand:
A clock has two hands, the smaller one is called the hour hand or
short hand while the larger one is called minute hand or long
hand.
Note the following:
i.
In 60 minutes, the minute hand gains 55 minutes on
the hour on the hour hand.
ii.
In every hour, both the hands coincide once.
iii.
The hands are in the same straight line when they
are coincident or opposite to each other.
iv.
When the two hands are at right angles, they are 15
minute spaces apart.
v.
When the hands are in opposite directions, they are
30 minute spaces apart.
vi.
Angle traced by hour hand in 12 hrs = 360°
vii.
Angle traced by minute hand in 60 min. = 360°.
viii.
If a watch or a clock indicates 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 too slow.
CLOCKS Problems
1.Find the angle between the hands of a clock when the time is 3:20
a)20 b)30 c)40 d)50
1.Find the angle between the hands of a clock when the time is 3:20
a)20 b)30 c)40 d)50
2.At what time between 4 and 5'o clock will the 2 hands of a clock be at an angle of 60 degrees with each other?
a)4:10 10/11 b)4:32 8/11 c)both a and b d)none of these
3.Find the time at which the hands of a clock are at right angles between 7 and 8'o clock?
a)7:21 9/11 b)7:54 6/11 c)both a & b d)none of these
4.Find the time at which the hands of a clock are exactly opposite directions between 8 and 9'o clock?
a)8:10 10/11 b)8:02 c)8:3/11 d)none of these
5.At what time between 2 and 3'o clock are the hands of a clock together?
a)2:10 b)2:10 10/11 c)2:10 10/12 d)none
6.In 24 hours,how many times do the two hands of a clock coincide?
a)20 times b)21 times c)22 times d)23 times
7.If the hands of a clock coincide every 65 minutes,how much time does the clock gain or lose per day?
a)10 100/146 b)10 100/145 c)10 100/156 d)10 100/143
8.In a country R,clocks are manufactured in a special way.The total area covered by the hour hand in 2 days is 2/3rd of the total area covered by the minute hand in one day.What is the ratio of the length of the minute
hand to the length of the hour hand?
a)1:2 b)2:1 c)4:1 d)1:4
a)1:2 b)2:1 c)4:1 d)1:4
9.There are two clocks,which are set to correct time on sunday at 12 noon.The first clock gains 2 1/2 minutes every hour while the second clock loses 1 1/2 minutes every hour.When will they be 2 hours apart?
a)Monday 9 p.m b)Tuesday 12 midnight c)Monday 6 p.m d)Tuesday 6 a.m
10.A watch which is set correctly at 12 noon on sunday shows 6:20 a.m on Monday when the correct time is 6:00 a.m.If the correct time is 6:00 p.m. on tuesday, what time does the clock show?
a)6:45 p.m b)7:00 p.m c)7:30 p.m d)8:00 p.m
11.At what time between 1 and 2'o clock are the two hands coincident?
a)1:12 5/11 b)1:07 5/11 c)1:05 5/11 d)1:08 5/11
12. Ajay started a test at a certain time between 5 and 6 and ended between 6 and 7. He observed that the minutes and hours hands when he ended the test had inter-changed their positions with those when he started.How much time did he take for the test?
a)52 3/11 b)55 5/13 c)47 4/9 d)45 min
13.A clock is started at noon.By 10 minutes past 5,the hour hand has turned through
a)145 deg b)150 deg c)155 deg d)160 deg
14.An accurate clock shows 8'o clock in the morning. Through how many degrees will the hour hand rotate when the clock show 2'o clock in the afternoon?
a)144 deg b)150 deg c)168 deg d)180 deg
15.At 3:40 the hour hand and the minute hand of a clock form an angle of
a)120 b)125 c)130 d)135
16.The angle between the minute hand and the hour hand of a
clock when the time is 8:30 is
a)80 b)75 c)60 d)105
a)80 b)75 c)60 d)105
17.The angle between the minute hand and the hour hand of a clock when the time is 4:20 is
a)0 b)10 c)5 d)20
18.At what angle the hands of a clock are inclined at 15 minutes past 5?
a)58 1/2 b)64 c)67 1/2 d)72 1/2
19.The reflex angle between the hands of a clock at 10:25 is
a)180 b)192 1/2 c)195 d)197 1/2
20.How many times do the hands of a clock coincide in a day?
a)20 b)21 c)22 d)24
21.How many times do the hands of a clock are straight?
a)22 b)24 c)44 d)48
22.How many times are theh hands of a clock at right angle in a day?
a)22 b)24 c)44 d)48
23.How many times in a day,are the hands of a clock in straight line but opposite in direction?
a)20 b)22 c)24 d)48
24.How much does a watch lose per day,if its hands coincide every 60 minutes?
a)32 8/11 b)36 5/11 c)90 min d)96 min
25.At what time,in minutes , between 3'o clock and 4'o clock , both the needles will coincide each other?
a)5 1/11 b)12 4/11 c)13 4/11 d)16 4/11
26.At what time between 9 and 10'o clock will the hands of a watch be together?
a)45 min past 9 b)50 min past 9 c)49 1/11past9 d)48 2/11 past 9
27.At what time between 7 and 8'o clock will the hands of a clock be in the same straight line but,not together?
a)5 min.past 7 b)5 2/11 past 7 c)5 3/11 past 7 d)5 5/11 past 7
28.At what time between 4 and 5'o clock will the handle of a watch point to opposite directions?
a)45 min past 4 b)40 min past 4 c)50 4/11 past 4 d)54 6/11 min past4
29.At what time between 5:30 and 6 will the hands of a clock be at right angles?
a)43 5/11 b)43 7/11 past 5 c)cannot be determined d)none
30.A watch which gains uniformly in 2 min low at noon on monday and is 4 min.48sec fast at 2 pp.m.on the following monday.when was it correct?
a)2 p.m on tuesday
b)2 p.m on wednesday
c)3 p.m on thursday
d)1 p.m on friday
31.A watch which gains 5 seconds in 3 minutes was set right at 7 a.m.In the afternoon of the same day,when the watch indicated quarter past 4'o clock,the true time is
a)59 7/12 past 3 b)4 p.m c)5 p.m d)7 p.m
32.A clock is set right at 8 a.m.The clock gains 10 minutes in 24 hours.What will be the true time whne the clock indicates 1 p.m on the following day?
a)48 min past 12 b)48 min c)47 min past 4 d)none
33.A clock is set right at 5 a.m.The clock loses 16 min in 24 hours.What will be the true time when the clock indicates 10 p.m on 4th day?
a)12 p.m b)1 p.m c)1 a.m d)11 p.m
34.The minute hand of a clock overtakes the hour hand at intervals of 65 min of the correct time.How much a day does the clock gain or lose?
a)10 10/43 in 24 hrs b)10 10/23 in 24 hrs c)10 10/34 in 24 hrs d)none
35.Find the angle between the hour hand and the minute hand of a clock when the time is 3:25
a)42 b)45 c)47 1/2 d)73
36.At what time between 2 and 3'o clock will the hands of a clock be together?
a)10 10/11 min past 2 b)10 10/11 past 3 c)10 10/11 past4 d)none
37.At what time between 4 and 5'o clock will the hands of a clock be at right angle?
a) 5 5/11 min past 4 b)38 2/11 min past 4 c)both a&b d)none
38.At what time between 4 and 5'o clock will the hands of a clock be at right angle?
a) 5 5/11 min past 4 b)38 2/11 min past 4 c)both a&b d)none
39.Find at what time between 8 and 9'o clock will the hands of a clock be in the same straight line but not together
a)10 10/11 min past 8 b)10 10/11 past7 c)10 10/11past2 d)none
40.At what time between 5 and 6'o clock are the hands of a clock 3 minutes apart?
a)31 5/11 min past 5
b)31 5/18 min past 5
c)31 5/19 min past 5
d)31 5/16 min past 5
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