CLOCKS
The dial of the clock is numbered from 1 to 12 in such a way that each subsequent number is equidistant
(15 minutes space apart) from the preceding number. It has two needles known as minute hand and hour hand.
The distance between two consecutive numbers is 5 minutes. It means that the circumference of the clock measures
60 minutes space. In this way, by traveling 60 minutes space, the minute hand gains 55 minutes on the hour hand.
Properties of Clock
1. In 60 minutes the minute hand gains 55 minutes on the hour hand.
2. A clock is said to be too fast when it shows time more than that of shown by a correct clock. Likewise, a
clock is said to be too slow when it shows time less than that of shown by a correct clock.
3. Both the hands of clock are at right angle (when the distance between two hand measures 90º) when they
are 15 minutes space apart. This situation occurs twice in one hour.
4. Both the hands of a clock are opposite to each other when they are 30 minutes space apart.
This situation occurs once in a hour.
5. The hands of the clock are in the same straight line when they are coincident or opposite to each other.
Ex.1 At what time between 7 and 8 will the hands of a clock be in the same striaght line, but not together ?
Sol. 
Figure (1) shows the positions of hands of the clock at 7 and figure (2) shows the positions of hands of clock
when both the hands are opposite in the stright line. From figure (1), it is clear that both the hands are 25 minute.
apart and to be in the stright line both the hands have to be 30 minutes apart. Now as per properties of the clock,
minute hand gains 55 minute space in 60 minutes.
Ex.2 At what time between 5.30 and 6 will the hands of a clock be at right angle ?
Sol. 
At 5 both the hands are 25 minutes apart and to be at right angle both the hands have to be 15 minutes apart
as shown in figure (2) and figure (3). Since we have to take the position of clock between 5.30 and 6 therefore,
the positions of hands of clock as per figure (3) is our answer. Now it is clear from figure (1) and figure (3)
that minute hand will have to travel (25 + 15) = 40 minutes space in order to form a right angle with the hour hand.
55 minutes space is gained in 60 minutes.
Therefore, 40 minutes space will be gained in
Ex.3 At what time between 4 and 5 will the hands of a watch point in opposite direction ?
(A) 45 minutes past 4
(B) 40 minutes past 4
Sol. 
As 4 o' clock both the hands are 20 minutes apart and for having in the opposite direction they have to be 30 minutes apart.
From figure (1) and (2) it is clear, that minute hand has to travel (20 + 30) minutes space in order to be in opposite direction to each other.
Now 55 minutes space is gained in
Ex.4 A watch, which gains uniformly, is 2 minutes slow at noon on monday, and in 4 minutes, 48
seconds fast at 2 P.M. on the following monday. What time it was 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
Sol. Time from monday noon (12 p.m.) to 2 p.m. the following monday = 7 days 2 hours = 170 hours
monday (12 p.m.) to 2 p.m. on the following monday or in other words, the watch gains minutes in 170 hours,
hours = 50 hours = 2 days 2 hours.
Therefore, the watch is correct after 2 days 2 hours from monday noon or at 2 p.m. on wednesday. So the correct option is (B).
Ex.5 A clock is set right at 5 a.m. The clock loses 16 minutes in 24 hours. What will be the right time when the
clock indicates 10 p.m. on the 4th day ?
(A) 11.15 p.m. (B) 11 p.m.
(C) 12 p.m. (D) 12.30 p.m
Sol. Time from 5 a.m. of a particular day to 10 p.m. on the 4th day is 89 hours. Now, the clock loses 16 minutes in 24 hours
or in other words we can say that 23 hours 44 minutes in 24 hours or in other 24 hours of the correct clock.
= 90 hours of the correct clock
or 89 hours of this clock = 90 hours of the
correct clock.
Therefore, it is clear that in 89 hours this clock loses 1 hour and hence the correct time is
11 p.m. When this clock shows 10 p.m.
Ex.6 How many times do the hands of a clock coincide in a day ?
(A) 24 (B) 22 (C) 21 (D) 20
Sol. From the properties of the clock we know that hands of a clock coincide once in every hour but between
11 o' clock and 1 o' clock they coincide only once. Therefore, the hands of a clock coincide 11 times in every
12 hours. Hence they will coincide (11 × 2) 22 times in 24 hours. So our answer is (B).
Ex.7 How many times are the hands of a clock at right angles in a day ?
(A) 24 (B) 48 (C) 22 (D) 44
Sol . We know that hands of a clock are at right angle twice in every hour. But two positions of the hands of clock
i.e. at 3 o' clock and 9 o' clock are indentical. So, they are at right angles 22 times in 12 hours and therefore,
in 24 hours or in a day they are at right angle 44 times. So the answer is (D).
Ex.8 Find what time between 8 and 9 o' clock will the hands of a clock be in the same stright line but not together ?
Sol.
Figure (1) shows the positions of the hands of the clock and it is clear that they are 20 minutes apart.
To be in the straight line they have to be 30 minutes apart. So the minute hand
will have to move 10 minutes space in order to be 30 minutes apart from the four hand. 65 minutes are gained in 60 minutes.
Ex.9 At what time between 3 and 4 o' clock will the hands of a clock coincide ?
Sol.
At 3 o'clock both the hands of the clock are 15 minutes apart. Hence in order to be together minute hand
will have to cover the distance of 15 minutes in order to find a position as shown in figure (2).
Now, 55 minutes are gained in 60 minutes.
Ex.10 A clock is set right at 8 a.m. The clock gain 10 minutes in 24 hours. What will be
the right time when the clock indicates 1 p.m. on the following day ?
(A) 11.40 p.m. (B) 12.48 p.m.
(C) 12 p.m. (D) 10 p.m.
Sol. Time from 8 a.m. of a particular day 1 p.m. on the following day = 29 hours. Now the clock gains 10 minutes
in 24 hours, it means that 24 hours 10 minute of this clock is equal to 24 hours of the correct clock.
= 28 hours, 48 minute of correct clock.
29 hours of this clock = 28 hours 48 minute of the correct clock.
It means that the clock in questions is 12 minute faster than the correct clock.
Therefore, when clock indicates 1 p.m. the correct time will be 48 minutes past 12.
Ex.11 At what time between 4 and 5 o' clock will the hands of a clock be at right angle ?
Sol. Between 4 and 5 o' clock the hands of the clock will be at right angle twice. First situation will occur when minute
hand is 5 minutes space behind the hour hand and second when minute hand is 15 minute space ahead of the hour hand.
Figure-2 shows the position when minute hand is 15 minute space behind the hour hand. To come at this
position minute hand has travelled 5 minute space from the position at 4 o' clock figure (1).
Now, 55 minutes are gained in 60 min.
Figure-3 shows the position when minte hand is 15 minutes space ahead the hour hand. To come
at this position minute hand has travelled 35 minute space from the position at 4 o'clock. (Figure-1).
Now, 55 minutes space are gained in 60 minutes
Now in our options 38 minutes past 4 is available as option (C). Hence it is our answer.
Ex.12 At what time between 5 and 6 are the hands of a clock coincident ?
(A) 22 minutes past 5
(B) 30 minutes past 5
Sol. From the figure we find what minute hand is 25 minutes space apart from hour hand. In order to coincide it has to gain 25 minute space.
Now, 55 minutes are gained by minute hand in 60 minutes.
25 minutes will be gained in × 25 = 27 minutes. So, the hands will coincide at 27 minutes past 5.
Ex.13 At what time between 9 and 10 will the hands of a watch be together ?
(A) 45 minutes past 9
(B) 50 minutes past 9
Sol. Both the hands are 15 minutes space part at 9 o'clock.
To be together between 9 and 10, minute hand has to gain 45 minutes.
Now, minute hand gains 55 minute in 60 minutes.
mintes
Therefore, the hands are together at minute past 9.
Ex.14 How many times do the hands of a clock point towards each other in a day ?
Sol . The hands of a clock point towards each other 11 times in every 12 hours (because between 5 and 7, they point
towards each other once at 6 o'clock). Therefore, in a day the hands points 22 times towards each other.
Ex.15 At what angle the hands of a clock are inclined at 15 minutes pasts ?
(A) 72º (B) 67º (C) 58º (D) 64º
Sol. At 15 minutes past 5, the minute hand is at 3 and hour hand slightly ahead of 5. Now, the angle through which hour hand shifts in 15
ASSIGNMENT
1. A tired worker slept at 7.45 p.m. If he rose at 12 noon, for how many hours did he sleep?
(A) 5 hours 15 min. (B) 16 hours 15 mind.
(C) 12 hours (D) 6 hours 45 min.
2. If a clock shows 04:28 then its mirror image will be ?
(A) 07:42 (B) 07:32
(C) 08:32 (D) 08:42
3. At what time between 2 and 3 O' clock the hands of a clock will make an angle of 160° ?
(A) 20 minutes past 2 (B) 30 minutes past 2
(C) 40 minutes past 2 (D) 50 minutes past 2
4. At a railway station a 24 hours watch loses 3 minutes in 4 hours. If it is set correctly on Sunday noon when will the watch show the correct time ?
(A) 6 pm after 40 days
(B) 12 noon after 75 days
(C) 12 pm after 100 days
(D) 12 noon after 80 days
5. A wrist watch which is running 12 minutes late on a Sunday noon is 6 minutes ahead of the correct time at 12 noon on the next Sunday. When is the clock 8 minutes ahead of time ?
(A) Thursday 10 am (B) Friday noon
(C) Friday 8 pm (D) Tuesday noon
6. A clock loses 2 minutes in a hour and another clock gains 2 minutes in every 2 hours. Both these clocks
are set correctly at a certain time on Sunday and both the clocks stop simultaneously on the next day with the
time shown being 9 am and 10 : 06 AM. what is the correct time at which they stopped ?
(A) 9 : 54 am (B) 9 : 44 pm
(C) 9 : 46 am (D) 9 : 44 am
7. Ramu purchased a second hand Swiss watch which is very costly. In this watch the minute-hand and
hour hand coincide after every 65 minutes. How much time does the watch lose or gain per day ?
(A) 4 min (B) 5 min
(C) 4 min, 20 sec (D) none of these
8. Out of the following four choices which does not show the coinciding of the hour hand and minute hand :
(A) 3 : 16 : 2 (B) 6 : 32 : 43
(C) 9 : 59 : 05 (D) 5 : 27 : 16
Direction : (9 to 10) A 12 dial clock has its minute hand defective. Whenever it touches dial 12, it immediately
falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12'O' clock in the noon.
9. What was the actual time when the minute hand of the clock touched dial 9 for the 5th time ?
(A) 2 : 15 (B) 3 : 00
(C) 5 : 15 (D) 6 : 45
10. If the actual time is 10 : 10, what is the position of the hour hand in that defective clock ?
(A) Between 2 and 3
(B) Between 4 and 5
(C) Between 10 and 11
(D) Between 3 and 4
ANSWER KEY
1) B 2) B 3) C 4) D 5) B
6) D 7) A 8) C 9) A 10) C