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.

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.

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

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°.

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

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

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°.

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.

Angle traced by hour hand in
17
hrs =

360
x
17

°
= 255°.
2
12
2

Angle traced by min. hand in 30 min. =

360
x 30

°
= 180°.
60

Required angle = (255 - 180)° = 75°.

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

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