Clock Aptitude Questions

Q9 At what angle the hands of a clock are inclined at 15 minutes past 5?

Angle traced by hour hand in	21	hrs =		360	x	21		°	=	157	1	°
	4			12		4					2

Angle traced by min. hand in 15 min. =		360	x 15		°	= 90°.
		60

Required angle =		157	1		°	- 90° = 67	1	°
			2				2

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?

Angle traced by the hour hand in 6 hours =360x 6°= 180°.12

Q2 The reflex angle between the hands of a clock at 10.25 is:

Angle traced by hour hand in	125	hrs =		360	x	125		°	= 312	1	°	.
	12			12		12				2

Angle traced by minute hand in 25 min =		360	x 25		°	= 150°.
		60

Reflex angle = 360° -		312	1	- 150		°	= 360° - 162	1	°	= 197	1°	.
			2					2			2

Q3 A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

Angle traced by hour hand in 12 hrs = 360°.

Angle traced by hour hand in 5 hrs 10 min. i.e.,

31

hrs =

360

x

31

°

= 155°.

Q4 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:

Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. =	37	hrs.
	4

3 min. 5 sec. of this clock = 3 min. of the correct clock.

	37	hrs of this clock =	1	hrs of the correct clock.
	720		20

	37	hrs of this clock =		1	x	720	x	37		hrs of the correct clock.
	4			20		37		4

= 9 hrs of the correct clock.

The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.

Q5 How much does a watch lose per day, if its hands coincide every 64 minutes?

55 min. spaces are covered in 60 min.

60 min. spaces are covered in		60	x 60	min.	= 65	5	min.
		55				11

Loss in 64 min. =		65	5	- 64		=	16	min.
			11				11

Loss in 24 hrs =		16	x	1	x 24 x 60	min.	=	32	8	min.
		11		64					11

Q6 At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?

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	x 5	min	= 5	5	min.
		55				11

Required time = 5	5	min. past 7.
	11

Q7 At what time between 5.30 and 6 will the hands of a clock be at right angles?

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	x 40	min	=	43	7	min.
		55					11

Required time = 43	7	min. past 5.
	11

Q8 The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

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°

Answer: Option B

Explanation:

Angle traced by hour hand in	13	hrs =		360	x	13		°	= 130°.
	3			12		3

Angle traced by min. hand in 20 min. =		360	x 20		°	= 120°.
		60

Required angle = (130 - 120)° = 10°.

Q10 At 3:40, the hour hand and the minute hand of a clock form an angle of:

Angle traced by hour hand in 12 hrs. = 360°.

Angle traced by it in	11	hrs =		360	x	11		°	= 110°.
	3			12		3

Angle traced by minute hand in 60 min. = 360°.

Angle traced by it in 40 min. =		360	x 40		°	= 240°.
		60

Required angle (240 - 110)° = 130°.