Clock Reasoning

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.
Thus, minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.
In 16 minutes, the minute hand gains (16×5.5)=88° over the hour hand.

In a clock, each minute makes 6°
So, 3 minutes will make 6×3=18°

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.
Thus, the minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.

At 2’o Clock, Minute Hand will be 10×6=60° behind the Hour Hand.
In 30 minutes, Minute Hand will gain 5.5°×30=165°.
The angle between Hour Hand and Minute Hand =165–60=105°.

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.
Thus, the minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.
At 8:00 pm, the angle between Minute Hand and Hour Hand will be 40×6=240°.
In 24 minutes, Minute Hand will gain 24×5.5=132°.
Required angle =240–132=108°.

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.
Thus, the minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.
At 5:00 pm, the angle between Minute Hand and Hour Hand will be 25×6=150°.
In 15 minutes, Minute Hand will gain 15×5.5=82.5°.
Required angle =150–82.5=67.5°.

The minute hand covers 6° in one minute and the hour hand covers 0.5° in one minute.
Thus, the minute hand will gain (6–0.5)=5.5° over the hour hand in one minute.
At 3 o'clock, the angle between Minute Hand and Hour Hand will be 15×6=90°.
In 25 minutes, Minute Hand will gain 25×5.5=137.5°.
Required angle =137.5–90=47.5°.

In order to strike 12, there are 11 intervals of equal time
=33÷3=11 seconds each
Therefore, to strike 6 it has 5 equal intervals,
it requires 5×3=15 seconds

When the hands of the clock are in the same straight line but not together, they are 30 minutes space apart.

At 7 o’clock, they are a 25 minutes space apart.
So, the minute hand will have to gain only 5 minutes space.

Minute hand gains 55 minutes space in 60 minutes.

5 minutes space will gain in:

Required time =5⁵⁄₁₁ minutes past 7

At 4 o’clock, the hands are 20 minutes space apart.
To be at right angles and that too between 4 and 5, the minute hand has to gain (20+15) =35 minutes space.
Minute hand gains 55 minutes space in 60 minutes.
35 minutes space will gain in:
(60/55)×35=38.18
Required time =4:38 approx.

At 5 o’clock, the hands are 25 minutes space apart.
To be at right angles and that too between 5:30 and 6, the minute hand has to gain (25+15) =40 minutes space.
Minute hand gains 55 minutes space in 60 minutes.
40 minutes space will gain in:

Required time =43⁷⁄₁₁ minutes past 5

At 4 o’clock, the hands of the watch are 20 minutes space apart.
To be in opposite directions, they must be 30 minutes space apart.
So, the Minute hand will have to gain (20+30)= 50 minutes space.
Minute hand gains 55 minutes space in 60 minutes.
50 minutes space will gain in:

Required time=54⁶⁄₁₁ minutes past 4

At 9 o’clock, the hands of the watch are 15 minutes space apart.
The hands will be opposite to each other when there is a space of 30 minutes between them.
This will happen when the Minute Hand gains (30–15)= 15 minutes space over Hour Hand.
Minute hand gains 55 minutes space in 60 minutes.
15 minutes space will gain in:
(60/55)×15 = 16⁴⁄₁₁
Required time= 16⁴⁄₁₁ minutes past 9

At 3 o’clock, the hands of the watch are 15 minutes space apart.
The hands will coincide with each other when there is a space of 0 minutes between them.
This will happen when the Minute Hand gains (15–0)=15 minutes space over Hour Hand.
Minute hand gains 55 minutes space in 60 minutes.
15 minutes space will gain in:
(60/55)×15 = 16⁴⁄₁₁
Required time= 16⁴⁄₁₁ minutes past 3

At 7 o’clock, the hands of the watch are 35 minutes space apart.
The hands will coincide with each other when there is a space of 0 minutes between them.
This will happen when the Minute Hand gains (35–0)=35 minutes space over Hour Hand.
Minute hand gains 55 minutes space in 60 minutes.
35 minutes space will gain in:
(60/55)×35 = 38.18
Required time= 38.18 minutes past 7

The minute hand of the accurate watch gains 55 minutes space in 60 minutes.
60 minutes space will cover in

Loss in 64 minutes

Loss in 24 hrs

Number of hours between 8 o’clock in the morning and 2 o’clock in the afternoon is 6.
Angle traced by the hour hand in 6 hours

Time from 5 am on a day to 10 pm on the 4th day is 89 hours.
Now, 23 hours 44 minutes of this clock are the same as 24 hours of the correct clock.
i.e., ³⁵⁶⁄₁₅ hours of this clock are the same as 24 hours of the correct clock.
Thus, 89 hours of this clock are the same as:

hours of the correct clock.
= 90 hrs of the correct clock.
So, the correct time is 11 pm.

Time from 7 am to quarter past 4
= 9 hours 15 minutes = 555 minutes
Now, (3 min +5 sec) = 37⁄12 minutes of this watch are the same as 3 minutes of the correct watch.
555 minutes of this watch will be the same as:
minutes of the correct watch.
= 9 hours of the correct watch.
The correct time is 9 hours after 7 am i.e., 4 pm

Time from 12 noon to 4.00 am, the next day
= 16 hours
The clock gains 15 minutes in 24 hours.
Therefore, in 16 hours, it will gain 10 minutes.
Hence, the time shown by the clock will be 4.10 am.

Time interval indicated by the incorrect clock from 1 pm to 6 pm
= 5 hours = 300 minutes
Now, 61 minutes of this watch are the same as 60 minutes of the correct watch.
300 minutes of this watch will be the same as:
(60/61)×300 minutes of the correct watch.
= 4⁵⁶⁄₆₁ hours of the correct watch.
The correct time is 4⁵⁶⁄₆₁ hours after 1 pm
Thus, the true-time = 55⁵⁄₆₁ minutes past 5

Time from noon on Sunday to 3 pm on Wednesday is 75 hours.
24 hours 2 minutes of the first clock are the same as 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 the correct one.
= 54000/721 hours = 74 hours 53.7 minutes.
Hence the answer is 2:54 pm.

Minute hand gains 55 minutes space in 60 minutes.

In a watch that is running correctly, the minute hand should cross the hour hand once in every:
60×(60/55) minutes.
So they should ideally cross 3 times once in:
3×60×(60/55) minutes =196.36 minutes.

But in the watch under consideration, they meet after every 3hr, 18 min and 15 seconds, i.e., 198.25 minutes.
Thus, the watch is actually losing time (as it is slower than the normal watch).

Hence 1 day (1440 min) of this watch will be:
1440×(196.36/198.25) = 1426.27 minutes.

Hence the amount of time lost the watch in one day:
=1440–1426.27=13.73 minutes
i.e., 13 min and 50s (approx).

Time between 10 am on Monday to 10:30 am on Sunday
= 6 days and ½ hrs = 144.5 hrs.

24 hr + 5 min = 289/12 hours of incorrect clock = 24 hours of correct time.
So, 144.5 hours of the incorrect clock
= 144.5×24/(289/12) hours of the correct time
= 144 hours i.e., the true time is 10 am on Sunday.

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

The watch gains

Now, 34/5 minutes are gained in 170 hrs.
So, 2 minutes are gained in

Watch is correct 2 days 2 hrs. after 12 pm on Monday i.e., it will be correct at 2 pm on Wednesday.