Question 1
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?
A. 144°
B. 150°
C. 168°
D. 180°
View Answer
Answer: Option D
Explanation:
Angle traced by the hour hand in 6 hours = ((360/12) x 6)° = 180°.
Question 2
The reflex angle between the hands of a clock at 10.25 is:
A. 180°
B. 192 1/2°
C. 195°
D. 197 1/2°
View Answer
Answer: Option D
Explanation:
Angle traced by hour hand in 125/12 hrs = (360/12 x 125/12)° = 312 1/2°
Angle traced by minute hand in 25 min = ((360/60) x 25)° = 150°.
Reflex angle = 360° - (312 1/2 - 150)° = 360° - 162 1/2)° = 197 1/2°
Question 3
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
A. 145°
B. 150°
C. 155°
D. 160°
View Answer
Answer: Option C
Explanation:
Angle traced by hour hand in 12 hrs = 360°
Angle traced by hour hand in 5 hrs 10 min. i.e., 31/6 hrs = (360/12 x 31/6)° = 155°.
Question 4
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:
A. 59 7/12 min. past 3
B. 4 p.m.
C. 58 7/11 min. past 3
D. 2 3/11 min. past 4
View Answer
Answer: Option B
Explanation:
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = 37/4 hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock.
= 37/720 hrs of this clock = 1/20 hrs of the correct clock.
= 37/4 hrs of this clock = (1/20 x 720/37 x 37/4) hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
Question 5
How much does a watch lose per day, if its hands coincide every 64 minutes?
A. 32 8/11 min.
B. 36 5/11 min.
C. 90 min.
D. 96 min.
View Answer
Answer: Option A
Explanation:
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 hrs = (16/11 x 1/64 x 24 x 60) min. = 32 8/11 min.
Question 6
At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
A. 5 min. past 7
B. 5 2/11 min. past 7
C. 5 3/11 min. past 7
D. 5 5/11 min. past 7
View Answer
Answer: Option D
Explanation:
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock, they are 25 min. spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
5 min. spaces are gained in (60/55 x 5)min = 5 5/11 min.
Required time = 5 5/11 min. past 7.
Question 7
At what time between 5.30 and 6 will the hands of a clock be at right angles?
A. 43 5/11 min. past 5
B. 43 7/11 min. past 5
C. 40 min. past 5
D. 45 min. past 5
View Answer
Answer: Option B
Explanation:
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.
Question 8
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
A. 0°
B. 10°
C. 5°
D. 20°
View Answer
Answer: Option B
Explanation:
Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)° = 130°.
Angle traced by min. hand in 20 min. = (360/60 x 20)° = 120°.
Required angle = (130 - 120)° = 10°.
Question 9
At what angle the hands of a clock are inclined at 15 minutes past 5?
A. 58 1/2°
B. 64°
C. 67 1/2°
D. 72 1/2°
View Answer
Answer: Option C
Explanation:
Angle traced by hour hand in 21/4 hrs = (360/12 x 21/4)° = 157 1/2°
Angle traced by min. hand in 15 min. = (360/60 x 15)° = 90°.
Required angle = 157 1/2° - 90° = 67 1/2°
Question 10
At 3:40, the hour hand and the minute hand of a clock form an angle of:
A. 120°
B. 125°
C. 130°
D. 135°
View Answer
Answer: Option C
Explanation:
Angle traced by hour hand in 12 hrs. = 360°.
Angle traced by it in 11/3 hrs = (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°.
Question 11
How many times are the hands of a clock at right angle in a day?
A. 22
B. 24
C. 44
D. 48
View Answer
Answer: Option C
Explanation:
In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Question 12
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
A. 80°
B. 75°
C. 60°
D. 105°
View Answer
Answer: Option B
Explanation:
Angle traced by hour hand in 17/2 hrs = (360/12 x 17/2)° = 255°.
Angle traced by min. hand in 30 min. = (360/60 x 30 )° = 180°.
Required angle = (255 - 180)° = 75°.
Question 13
How many times in a day, are the hands of a clock in straight line but opposite in direction?
A. 20
B. 22
C. 24
D. 48
View Answer
Answer: Option B
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Question 14
At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
A. 45 min. past 4
B. 40 min. past 4
C. 50 4/11 min. past 4
D. 54 6/11 min. past 4
View Answer
Answer: Option D
Explanation:
At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
50 min. spaces are gained in (60/55 x 50) min. or 54 6/11min.
Required time = 54 6/11 min. past 4.
Question 15
At what time between 9 and 10 o'clock will the hands of a watch be together?
A. 45 min. past 9
B. 50 min. past 9
C. 49 1/11 min. past 9
D. 48 2/11 min. past 9
View Answer
Answer: Option C
Explanation:
To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
45 min. spaces are gained in (60/55 x 45) min or 49 1/11 min.
The hands are together at 49 1/11 min. past 9.
Question 16
A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it 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
View Answer
Answer: Option B
Explanation:
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
The watch gains (2 + 4 4/5)min. or 34/5 min. in 170 hrs.
Now, 34/5 min. are gained in 170 hrs.
2 min. are gained in (170 x 5/34 x 2) hrs = 50 hrs.
Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.
Question 17
How many times in a day, the hands of a clock are straight?
A. 22
B. 24
C. 44
D. 48
View Answer
Answer: Option C
Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Question 18
How many times do the hands of a clock coincide in a day?
A. 20
B. 21
C. 22
D. 24
View Answer
Answer: Option C
Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
Question 19
At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
A. 5 1/11"
B. 12 4/11"
C. 13 4/11"
D. 16 4/11"
View Answer
Answer: Option D
Explanation:
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.
55 min. are gained in 60 min.
15 min. are gained in (60/55 x 15) min = 16 4/11 min.
The hands are coincident at 16 4/11 min. past 3.