The time gap between 3:00 a.m. to 11:00 a.m. is 8 hours.
Ci loses 4.5 x 8 = 36 minutes in 8 hours. Hence it shows 10:24 a.m.
C2 loses 1.5 x 8 = 12 minutes in 8 hours.
Hence it shows 10:48 a.m.
The clock C3 gains 2.5×8 = 20 minutes in 8 hours.
Hence it shows 11:20 a.m.
Ci and C2 differ by 24 minutes.
C2 and C3 differ by 32 minutes and
Ci and C3 differ by 56 minutes.

Time from noon on Sunday to 3 pm on Wednesday = 75 hours.
24 hours 2 minutes of the first clock= 24 hours of the correct one.
⇒ 1 hour of the first clock= 24 × (30/721) hours of correct one.
⇒ 75 hours of the first clock = 24 × 30 × (75/721) hours of correct one
= 54000/721 hours = 74 hours 53.7 min.
Hence the answer is 2:54 pm.

In this type of problems the formulae is
(5*x+ or – t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart

Case 1 : (5*x + t) * 12/11

(5*5 + 3) * 12/11

28 * 12/11 = 336/11= 31 5/11 min

therefore the hands will be 3 min apart at 31 5/11 min past 5.

Case 2 : (5*x – t) * 12/11

(5*5 -3 ) * 12/11

22 *12/11 = 24 min

therefore the hands will be 3 min apart at 24 min past 5

At 3 O’clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.

Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°

Hence, Angle between Hour and the Minute hand = ( 60 – 12.5 ) = 47.5°

Time from 5 a.m. on a day to 10 p.m. on 4th day is 89 hours.
Now, 23 hrs. 44 min. of this clock are the same as 24 hours of the correct clock.
i.e., ³⁵⁶⁄₁₅ hrs. of this clock = 24 hrs. of correct clock.
∴89 hrs. of this clock =hrs. of correct clock
= 90 hrs of correct clock.
So, the correct time is 11 p.m.

There are 3 intervals when the clock strikes 4

Time taken for 3 intervals = 9 seconds

Time taken for 1 interval  seconds

In order to strike 12, there are 11 intervals.

Hence time needed  seconds

To be together between 9 and 10 O’clock, the minute hand has to gain 45min.
spaces 55min. spaces are gained in 60min.
45min.spaces are gained in (60/55 × 45) min. or 49 1/11 min.
The hands are together at 49 1/11 min. past 9.

The speed of hour hand is 0.5 dpm (Degree per Minute)
And the speed of minute hand is 6 dpm.
So, 300 degree traverse by minute hand in 300/6 = 50 Minutes.
Thus, angle moved by the hour hand in 50 minutes is 50/0.5 = 25° degrees.

In a correct clock, the minute hand gains 55 min. spaces over
the hour hand in 60 min.
55 min. are gained in 60 min.

60 min. are gained in (60/55) X 60=65(5/11) min

But, they are together after 65 min.

Therefore, Gain in 65 min=(65(5/11)-65) =5/11.

Gain in 24 hours = (5/11) X ((60 X 24)/65)=10(10/43) min.

Therefore, The clock gains 10(10/43) min. in a day.

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

∴ 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.

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).

AM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

PM

12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55

The hands overlap about every 65 minutes, not every 60 minutes.

 The hands coincide 22 times in a day.

Angle traced by the hour hand in 6 hours=(360/12)*6

In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minutes, the minute hand gains 330° over the hour hand.
∴ In 16 minutes, the minute hand gains over the hour hand by 

The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 ‘o clock only.

Hence the hands point in the opposite directions 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).