Clock

Question:
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	min. past 3
	12

[B].

4 p.m.

[C].

58	7	min. past 3
	11

[D].

2	3	min. past 4
	11

Answer: Option B

Explanation:

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.

Question:
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

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	min.	or	34	min. in 170 hrs.
			5			5

Now,	34	min. are gained in 170 hrs.
	5

2 min. are gained in		170 x	5	x 2	hrs	= 50 hrs.
			34

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

[A].

43	5	min. past 5
	11

[B].

43	7	min. past 5
	11

[C].

40 min. past 5

[D].

45 min. past 5

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	x 40	min	=	43	7	min.
		55					11

Required time = 43	7	min. past 5.
	11

Question:
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	min. past 4
	11

[D].

54	6	min. past 4
	11

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	x 50	min. or 54	6	min.
		55			11

Required time = 54	6	min. past 4.
	11

Question: 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	min. past 7
	11

[C].

5	3	min. past 7
	11

[D].

5	5	min. past 7
	11

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	x 5	min	= 5	5	min.
		55				11

Required time = 5	5	min. past 7.
	11

Question:
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	min. past 9
	11

[D].

48	2	min. past 9
	11

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	x 45	min or 49	1	min.
		55			11

The hands are together at 49	1	min. past 9.
	11

Question:
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

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	x 15	min	=	16	4	min.
		55					11

The hands are coincident at 16	4	min. past 3.
	11

Question: How much does a watch lose per day, if its hands coincide every 64 minutes?
[A].

32	8	min.
	11

[B].

36	5	min.
	11

[C].

90 min.

[D].

96 min.

Answer: Option A

Explanation:

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

Question:
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

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:
How many times are the hands of a clock at right angle in a day?

[A].

22

[B].

24

[C].

44

[D].

48

Answer: Option C

Explanation:

In 12 hours, they are at right angles 22 times.

In 24 hours, they are at right angles 44 times.