Q1)-An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Q2)-How much does a watch lose per day, if its hands coincide every 64 minutes?
Q3)-A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
Q4)-A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
Q5)-At what time between 5.30 and 6 will the hands of a clock be at right angles?
Q6)-How many times will the hands of a clock coincide in a day?
Q7)-The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Q8)-At 3:40, the hour hand and the minute hand of a clock form an angle of:
Q9)-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:
Q10)-How many times are the hands of a clock at right angle in a day?
154°
180°
170°
160°
Ans.- B
As we know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6 x (360 / 12 ) = 180
As we know that angle traced by hour hand in 12 hrs = 360°
From 8 to 2, there are 6 hours.
Angle traced by the hour hand in 6 hours = 6 x (360 / 12 ) = 180
Q2)-How much does a watch lose per day, if its hands coincide every 64 minutes?
32(8/11) min
36(5/11) min
90 min
96 min
Ans.- A
55 min spaces are covered in 60 min.
60 min spaces are covered in [ 60/55 x 60 ] min = 65(5/11) min
Loss in 64 min= [ 65(5/11) - 64 ] = 16/11 min
Loss in 24 hours = { 16/11 x 1/64 x 24 x 60 } min = 32(8/11) min
55 min spaces are covered in 60 min.
60 min spaces are covered in [ 60/55 x 60 ] min = 65(5/11) min
Loss in 64 min= [ 65(5/11) - 64 ] = 16/11 min
Loss in 24 hours = { 16/11 x 1/64 x 24 x 60 } min = 32(8/11) min
Q3)-A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
46 min. past 12.
47 min. past 12.
48 min. past 12.
45 min. past 12.
Ans.- C
Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock. 145/6 hours of this clock = 24 hours of the correct clock.
29 hours of this clock = ( 24 x 6/145 x 29) hours of the correct clock = 28 hours 48 min of the correct clock.
Therefore , the correct time is 28 hours 48 min after 8 am.
This is 48 min past 12
Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock. 145/6 hours of this clock = 24 hours of the correct clock.
29 hours of this clock = ( 24 x 6/145 x 29) hours of the correct clock = 28 hours 48 min of the correct clock.
Therefore , the correct time is 28 hours 48 min after 8 am.
This is 48 min past 12
Q4)-A clock is started at noon. By 10 minutes past 5, the hour hand has turned through
155°
145°
152°
140°
Ans.- A
We know that angle traced by hour hand in 12 hrs = 360°
Time duration from noon to 10 minutes past 5 = 5 hours 10 minutes = 31/6 hours
Hence the angle traced by hour hand from noon to 10 minutes past 5 = 31/6 x 360/12 = 31 x 5 =155
We know that angle traced by hour hand in 12 hrs = 360°
Time duration from noon to 10 minutes past 5 = 5 hours 10 minutes = 31/6 hours
Hence the angle traced by hour hand from noon to 10 minutes past 5 = 31/6 x 360/12 = 31 x 5 =155
Q5)-At what time between 5.30 and 6 will the hands of a clock be at right angles?
43 min past 5
43(7/11) min past 5
40 min past 5
38 min past 5
Ans.- B
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in (60/55 x 40)min = 43(7/11) min
Required time = 43(7/11)min. past 5.
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in (60/55 x 40)min = 43(7/11) min
Required time = 43(7/11)min. past 5.
Q6)-How many times will the hands of a clock coincide in a day?
24
20
21
22
Ans.- D
The hands of a clock coincide 11 times in every 12 hours (Between 11 and 1, they coincide only once, at 12 o'clock).
12:00 am
1:05 am
2:11 am
3:16 am
4:22 am
5:27 am
6:33 am
7:38 am
8:44 am
9:49 am
10:55 am
12:00 pm
1:05 pm
2:11 pm
3:16 pm
4:22 pm
5:27 pm
6:33 pm
7:38 pm
8:44 pm
9:49 pm
10:55 pm
Hence the hands coincide 22 times in a day.
This is already given as a formula and it's is better to learn the answer by heart as 22 which can save time in competitive exams.(However you should know the theory behind).
The hands of a clock coincide 11 times in every 12 hours (Between 11 and 1, they coincide only once, at 12 o'clock).
12:00 am
1:05 am
2:11 am
3:16 am
4:22 am
5:27 am
6:33 am
7:38 am
8:44 am
9:49 am
10:55 am
12:00 pm
1:05 pm
2:11 pm
3:16 pm
4:22 pm
5:27 pm
6:33 pm
7:38 pm
8:44 pm
9:49 pm
10:55 pm
Hence the hands coincide 22 times in a day.
This is already given as a formula and it's is better to learn the answer by heart as 22 which can save time in competitive exams.(However you should know the theory behind).
Q7)-The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
0º
10º
5º
20º
Ans.- B
Angle traced by hour hand in 13/3 hours = ( 360/12 x 13/3) = 130
Angle traced by min hand in 20 min = ( 360/60 x 20 ) =120
Required angle = (130-120)=10
Angle traced by hour hand in 13/3 hours = ( 360/12 x 13/3) = 130
Angle traced by min hand in 20 min = ( 360/60 x 20 ) =120
Required angle = (130-120)=10
Q8)-At 3:40, the hour hand and the minute hand of a clock form an angle of:
120°
125°
130°
135°
Ans.- C
Angle traced by hour hand in 12 hrs. = 360°.
Angle traced by it in 11/3 hours = ( 360/12 x 11/3 ) =110
Angle traced by minute hand in 60 min =360
Angle traced by it in 40 min = (360/60 x 40 ) = 240
Required angle (240-110) = 130
Angle traced by hour hand in 12 hrs. = 360°.
Angle traced by it in 11/3 hours = ( 360/12 x 11/3 ) =110
Angle traced by minute hand in 60 min =360
Angle traced by it in 40 min = (360/60 x 40 ) = 240
Required angle (240-110) = 130
Q9)-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:
4 pm
5 pm
6 pm
7 pm
Ans.- A
Time from 7 am to 4.15 pm = 9 hrs 15 min = 37/4 hrs
3 min 5 sec of this clock = 3 min of the correct clock.
37/720 hours of this clock = 1/20 hours of the correct clock
37/4 hours of clock = (1/20 x 720/37 x 37/4) hours of the correct clock.
= 9 hours of the correct clock.
The correct time is 9 hours after 7 am i.e 4 pm
Time from 7 am to 4.15 pm = 9 hrs 15 min = 37/4 hrs
3 min 5 sec of this clock = 3 min of the correct clock.
37/720 hours of this clock = 1/20 hours of the correct clock
37/4 hours of clock = (1/20 x 720/37 x 37/4) hours of the correct clock.
= 9 hours of the correct clock.
The correct time is 9 hours after 7 am i.e 4 pm
Q10)-How many times are the hands of a clock at right angle in a day?
48
44
24
22
Ans.- B
In 12 hours, hands of a clock are at right angles 22 times.
In 24 hours, hands of a clock are at right angles 44 times.
In 12 hours, hands of a clock are at right angles 22 times.
In 24 hours, hands of a clock are at right angles 44 times.
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