22. Clocks

Sakshi Education

Introduction:
For solving the problems on clocks the following points will be helpful
1) Minutes hand covers 360^o in 1 hour, i.e., in 60 minutes. Hence, minutes hand covers 6^° per minute. (360/60 = 6^°)
2) Hour hand covers 360^o in 12 hours, hence hour hand covers 30^o per hour i.e., ½ per minute (30/60 = ½^o)

3) Hours hand and minute’s hand coincide with each other:
12 hours 24 hours/1day
a. 0^o with each other (i.e.., they coincide with each other) 11 times 22 times
b. 180^o with each other (i.e., they lie on the same straight line) 11 times 22 times
c. Remaining all angles except 0^o & 180^o 22 times 44 times

Note:
1. The time gap between any two coincidences is minutes
Correct time:-
If a clock is said to be a correct time then the time gap between any two coincidences is

minutes.

If a clocks coincidence time is less than min’s then the clock is going fast (or) gaining time.
If a clock coincidence time is greater than min’s then the clock is going slow (or) losing time

To calculate the angle between two hands of a clock

Ex: 1 Find the angle between the min’s hand and hour’s hand of a clock at 5 hours 20 min’s?
(a) 45^o
(b) 40^o
(c) 30^o
(d) 20^o
Sol: Here we have hours = 5 hrs; minute = 20 min

=|110 - 150| = |-40|= 400
: Angle between the two hand is 40^o
Ans: b

Ex: 2 At what time between 2 and 3 0’ clock will the hands of a clock be together?
Sol: At 2 0’clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min. spaces apart
To be together, the minute hand must gain 10 minutes over the hour hand.
Now, 55 minutes are gained by it in 60 min.
10 minutes will be gained in

The hand will coincide at

past 2.

Ex: 3 At what time between 4 and 5 0’clock will the hands of a clock be at right angle?
Sol: At 4 0’ clock the minute hand will be 20 min. spaces behind the hour hand.
Now, when the two hands are at right angles, they are 15 min, spaces apart
So, they are at right angles in following two cases.

Case 1.when minute hand is 15 min. spaces behind the hour hand:
In this case min, hand will have to gain (20-15) = 5 minute spaces.
55 min. spaces are gained by it in 60 min.
5 min. spaces will be gained by it in

They are at right angles at

past 4.

Case II: When the minute hand is 15 min. spaces ahead of the hour hand:
To be in this position, the minute hand will have to gain (20+15) = 35 minute spaces.
55 min. spaces are gained in 60 min.
35 min, spaces are gained in

They are at right angles at

past 4.

Ex: 4 Find at what time between 8 and 9 0’ clock will the hands of a clock be in the same straight line but not together.
Sol: At 8 0’ clock, the hour hand is at 8 and the minute hand is at 12, i.e., the two hands are 20 min. space apart.
To be in the same straight line but not together they will be 30 minute spaces apart
So, the minute hand will have to gain (30-20) = 10 minute spaces over the hour hand.
55 minute spaces are gained in 60 min
10 minute spaces will be gained in

The hands will be in the same straight line but not together at

past 8.

Ex: 5 The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much a day does the clock gain or lose?
Sol: In a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour hand
55 min. are gained in 60 min.
60 min. are gained in

But, they are together after 65 min.
Gain in 65 min.

Gain in 24 hours

The clock gains

minutes in 24 hours.

Ex: 6 A watch which gains uniformly, is 5 min. slow at 8 0’ clock in the morning on Sunday and it is 5 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
Sol: Time from 8 a.m. on Sunday to 8 p.m on following Sunday = 7 days 12 hours = 180 hours
The watch gains

in 180 hrs.
Now

min, are gained in 180 hrs.
5 min, are gained in

hrs. = 83 hrs 20 min = 3 days 11 hrs 20 min.
Watch is correct 3 days 11 hrs 20 min after 8 a.m. of Sunday
It will be correct at 20 min. past 7 P.M. on Wednesday

EXERCISE

What was the angle covered by the hour hand in 15 minutes?
(a) 45^o
(b) 30^o
(c) 71/2^o
(d) 90^o
(e) 15^o
By how many degrees will the minute hand move, in the same time, in which the hour hand moves by 12^o?
(a) 144^o
(b) 6^o
(c) 24^o
(d) 120^o
(e) 140^o
What is the angle between the two hands of a clock, when it shows 30 min past 3 0’ clock?
(a) 110^o
(b) 75^o
(c) 60^o
(d) 105^o
(e) 90^o
What is the angle between the two hands of a clock at 45 min past 6 0’ clock?
(a) 43 ½^o
(b) 135^o
(c) 75 ½^o
(d) 67 ½^o
(e) 90^o
What is the angle between the two hands of a clock 20 min’s past 11 0’ clock?
(a) 145^o
(b) 140^o
(c) 120^o
(d) 130^o
(e) 180^o
At what time between 4 0’ clock & 5 0’ clock are the hands of a clock together?
(a) 4 hr 21 min
(b) 5 hr 21 min
(c) 4 hr 20 20/11 min
(d) 4 hr 15min
(e) None
At what time between 8 0’ clock & 9 0’ clock will the hands of a clock coincide?
(a) 8 hr 23 2/11
(b) 8 hr 51 3/11min
(c) 8 hr 43 7/11 min
(d) 8 hr 17 2/11 min
(e) Can’t be determined
At what time between 4 0’ clock & 5 0’ clock are the hands of a clock in the opposite directions?
(a) 4 hr 54 6/11 min
(b) 4 hr 11 10/11 min
(c) 4 hr 38 2/11 min
(d) 4 hr 43 7/11 min
(e) Both A & B
For how many times, the two hands of a clock overlap in 12 hours?
(a) 12
(b) 11
(c) 10
(d) 14
(e) 22
For how many times, the two hands of a clock overlap in 24 hours
(a) 22
(b) 20
(c) 24
(d) 12
(e) 11
For how many times, the two hands of a clock perpendicular to each other in a day?
(a) 40
(b) 48
(c) 44
(d) 22
(e) 11
For how many times, the two hands of a clock make an angle of 600 in a 12 hours
(a) 11
(b) 22
(c) 44
(d) 48
(e) 40
What is the time shown by a clock if the hour hand is in between the hour division 7 and 8, and the angle between the two hand is 50^o
(a) 7 Hr 29 1/11min
(b) 7 hr 47 3/11 min
(c) 7 Hr 43 7/11 min
(d) 7 Hr 32 9/11 min
(e) Both A & B
What is the time shown by a clock of the hour hand is in between 5 0’ clock & 6 0’ clock and the angle between the two hands is 100^o
(a) 5 hr 45 5/11 min
(b) 5 hr 43 7/11 min
(c) 5 Hr 9 1/11min
(d) 5 hr 35 6/11 min
(e) Both a & c
Two clocks are having the correct time at 8 am one clock loses one minute per hour while the other gains two min’s per hour. At 5 Pm on the same day, by how much time will the two clocks differ?
(a) 30 min
(b) 27 min
(c) 24 min
(d) 32 min
(e) 26 min
A watch which loses uniformly was observed to be 4 minutes fast at 8 am on a Sunday and two minutes slow at 2 pm on the next days, Monday. When did the watch show the correct time?
(a) 2 am on Monday
(b) 4 am on Monday
(c) 3 am on Monday
(d) 8 am on Monday
(e) 12 am on Monday
A watch which gains uniformly was observed to be five minutes slow at 10 am on a Friday & 7 minutes fast at 10 pm on the subsequent Sunday. When did the watch show the correct time?
(a) 11 am on Saturday
(b) 1 pm on Saturday
(c) 10 am on Saturday
(d) 1am on Saturday
(e) None of these
A clock strikes once at 1 0’ clock, twice at 2 0’clcok, three times at 3 0’clock and so on. If it takes 4 seconds to strike at 4 0’ clock. Find the time taken by it to strike at 10 0’ clock
(a) 16 sec
(b) 18 sec
(c) 24 sec
(d) 12 sec
(e) 15 sec
What is the mirror image of a clock when it is shows 5 hr 20 min?
(a) 6 Hr 20 min
(b) 7 hr 40 min
(c) 6 hr 40 min
(d) 7 hr 20 min
(e) None of these
The reflection of a wall clock in mirror is showing the time as 4 hr 44 min. what is the actual time?
(a) 6 hr 16 min
(b) 8 hr 16 min
(c) 7 hr 16 min
(d) 8 hr 14 min
(d) None of these
The min’s hand of a clock over takes the hour hand at intervals of 65 min’s of correct time. How much does the clock lose (or) gain in a day?
(a) 11 11/143min gain
(b) 10 10/143 min gain
(c) 9 9/143 min gain
(d) both a & b
(e) None of these
The min’s hand of a clock overtakes the hour hand at intervals of 64 min’s of correct time. How much does the clock lose (or) gain in a day?
(a) 23 7/11min fast / gain
(b) 30 6/11 min fast/gain
(c) 32 8/11 min fast/gain
(d) both a & c
(e) None of these
The min’s hand of a clock over takes the hour hand at intervals of 66 min’s of correct time. How much does the clock lose (or) gain in a day?
(a) 11 109/121 min gain
(b) 11 109/121 min lose
(c) 10 109/121min gain
(d) 10 109/121 min lose
(e) None of these
What is the mirror image of the clock, if the time is 4:30?
(a) 7:30
(b) 6:30
(c) 5:30
(d) 8:20
(e) None of these
A clock which loses time uniformly was observed to be 3 min’s fast at 3:00 pm on a Wednesday. On the sub-sequent Friday at 10 pm the clock was 8 min’s slow. When did the clock shows the correct time?
(a) Thursday 8am
(b) Thursday 6 pm
(c) Thursday 6 am
(d) Thursday 8 pm
(e) None of these