# Ch.18 :- Clocks :- Exercise 1

1. 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) 1010/11 minute past 8
(b) 5010/11 minute past 8
(c) 1012/11 minute past 8
(d) 10 minute past 8

Ans.(a)

Fig. shows the positions of the hands of the clock and it is clear that they are 20 minute apart. To be in the straight line they have to be 30 minute apart. So the minute hand will have to move 10 minute space in
order to be 30 minute apart from hour hand.
55 minute are gained in 60 minute
10 minute will be gained in
60/55 x 10 = 12/11 x 10 minute

Therefore; the hands will be at right angle but not together at 1010/11 minute past 8.

2. At what time between 3 and 4 O’clock will the hands of a clock coincide?
(a) 15 minute past 3
(b) 1510/11 minute past 3
(c) 1012/11 minute past 3
(d) 164/11 minute past 3

Ans.(d)

At 3 O’clock both the hands of the cock are 15 minute apart. Hence in order to be together, minute hand will have to cover the distance of 15 minute in order to find a position as shown in Fig.
Now, 55 minute are gained in 60 minute
15 minute will be gained in(60/55 x 15)minute = (12/11 x 15)minute

=180/11 or 164/11 minute

Therefore, the hands will coincide at 164/11 minute past 3.

3. A clock is set right at 8 am. The clock gains 10 minute in 24 hours. What will be the right time when the clock indicates 1 pm on the following day?
(a) 11.40 pm
(b) 12.48 pm
(c) 12 pm
(d) 10 pm

Ans.(b)

Time from 8 am of a particular day to 1 pm on the following day = 29 hours
Now the clock gains 10 minute in 24 hrs, it means that
24 hrs 10 minute of this clock is equal to 24 hours of the correct clock.
145/6 hours of this clock = 24 hours of the correct clock.
29 hours of this clock = 24/145 x 6 x 29
= 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 question is 12 minute faster than the correct clock. Therefore, when clock indicates
1 pm the correct time will be 48 minute past 12.

4. At what time between 4 and 5 O’clock will the hands of a clock be at right angle?
(a) 30 minute past 4
(b) 163/4 minute past 4
(c) 382/11 minute past 4
(d) 33 minute past 4

Ans.(c)

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 15 minute space behind the hour hand and second when minute hand is 15 minute space

Fig. 18.13 shows the position when minute hand is 15 minute spaces behind the hour hand. To come at this
position minute hand has travelled 5 minute space from the position at 4 O’clock. Fig.18.12
Now, 55 minute are gained in 60 minute
5 minute will be gained in60/55 x 5 =60/11
It means that hands of the clock will be at right angle at
55/11 1 minute past 5.
Fig. 18.14 shows the position when minute hand is 15 minute space ahead the hour hand. To come at this position minute hand has travelled 35 minute spaces from the position at 4 O’clock. Fig. 18.12.
Now, 55 minute space are gained in 60 minute
35 minute spaces will be gained in 60/55 x 35 = 420/11minut

= 382/11minute
It means that second position will come at 382/11minute past 4.
Now, in the options 382/11minute past 4 is available as
option (c). Hence, it is the correct answer.

5. At what time between 5 and 6 are the hands of a clock coincident?
(a) 22 minute past 5
(b) 30 minute past 5
(c) 228/11 minute past 5
(d) 273/11 minute past 5

Ans.(d)

From the Fig. 18.15 we find that minute hand is 25 minute spaces apart from hour hand. In order to coincide it has to gain 25 minute spaces.
Now, 55 minute are gained by
minute hand in 60 minute Fig. 18.15
25 minute will be gained in
60/55 x 25 = 27 3/11 minute
So, the hands will coincide at 27 3/11 minute past 5

6. At what time between 9 and 10 O’clock will the hands of a watch be together?
(a) 45 minute past 9
(b) 50 minute past 9
(c) 491/11 minute past 9
(d) 482/11 minute past 9

Ans.(c)

Both the hands are 15 minute space part at 9 O’clock. To be together between 9 and 10, minute hand has to gain 45 minute
Now, minute hand gains 55 minute 9 in 60 minute
It will gain 45 minute in
60/55 x 45 = 49 1/11 minute Fig. 18.16
Therefore, the hands are together at 49 1/11 minute past 9.

7. How many times do the hands of a clock point towards each other in a day?
(a) 24
(b) 20
(c) 12
(d) 22

Ans.(d)

The hands of a clock point towards each other 11.times in every 12 hour (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.

8. At what angle the hands of a clock are inclined at 15 minute past 5 ?
(a) 721/2°
(b) 671/2°
(c) 581/2°
(d) 64°