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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) 10^{10}/_{11} minute past 8

(b) 50^{10}/_{11} minute past 8

(c) 10^{12}/_{11} minute past 8

(d) 10 minute past 8

View Answer

**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 10^{10}/_{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) 15^{10}/_{11} minute past 3

(c) 10^{12}/_{11} minute past 3

(d) 16^{4}/_{11} minute past 3

View Answer

**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 16^{4}/_{11} minute

Therefore, the hands will coincide at 16^{4}/_{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

View Answer

**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) 16^{3}/_{4} minute past 4

(c) 38^{2}/_{11} minute past 4

(d) 33 minute past 4

View Answer

**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

ahead of the hour hand.

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 in^{60}/_{55} x 5 =^{60}/_{11}

It means that hands of the clock will be at right angle at

5^{5}/_{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}/_{11}minut

= 38^{2}/_{11}minute

It means that second position will come at 38^{2}/_{11}minute past 4.

Now, in the options 38^{2}/_{11}minute 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) 22^{8}/_{11} minute past 5

(d) 27^{3}/_{11} minute past 5

View Answer

**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) 49^{1}/_{11} minute past 9

(d) 48^{2}/_{11} minute past 9

View Answer

**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

View Answer

**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) 72^{1}/_{2}°

(b) 67^{1}/_{2}°

(c) 58^{1}/_{2}°

(d) 64°

View Answer

**Ans.(b)**
At 15 minute past 5, the minute hand is at 3 and hour hand slightly ahead of s.

Now, the angle through which hour hand shifts in 15

minute = (15^{1}/_{2})° = 7^{1}/_{2}°

∴ Angle at 15 minute past 5 = (60 + 7^{1}/_{2}°) = 67^{1}/_{2}°