At what time between 9 and 10 o'clock will the hands of a watch be together?

- Option 1)
45 min. past 9

- Option 2)
50 min. past 9

- Option 3)
min. past 9

- Option 4)
48 min. past 9

- Option 5)
min. past 9

At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?

- Option 1)
45 min. past 4

- Option 2)
None of these

- Option 3)
min. past 4

- Option 4)
min. past 4

- Option 5)
40 min. past 4

How many times in a day, are the hands of a clock in straight line but opposite in direction?

- Option 1)
26

- Option 2)
22

- Option 3)
24

- Option 4)
48

- Option 5)
20

The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:

- Option 1)
85º

- Option 2)
75º

- Option 3)
60º

- Option 4)
105º

- Option 5)
80º

Formula to calculate angle = (11m/2) - 30h
Where, m = minute & h = hour
So, Angle when the time is 8:30 = (11 x 30/2) - 30 x 8
= 165 - 240 => -75 degree
Ignore the negative sign,
Angle = 75 degree

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

- Option 1)
5 min. past 7

- Option 2)
None of these

- Option 3)
min. past 7

- Option 4)
min. past 7

- Option 5)
min. past 7

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:

- Option 1)
min. past 3

- Option 2)
4 p.m.

- Option 3)
min. past 3

- Option 4)
5 p.m.

- Option 5)
min. past 3

Time difference between 7 AM to 4:15 PM = 9 Hours 15 Minutes or 37/4 hours
3 Minutes & 5 Seconds wrong time = 3 Minutes of actual time
37/12 Minutes wrong time = 3 Minutes of actual time
If we convert it into hours,
37/720 hours = 1/20 hours of actual time
37/4 hours of wrong time = 1/20 x 720/37 x 37/4 => 9 Hours
The Actual-time = 7 AM + 9 hours => 4 PM

The minute-hand of a clock overtakes the hour-hand at intervals of 65 minutes of the correct time. How much in a day does the clock gain or lose?

- Option 1)
- Option 2)
- Option 3)
None of these

- Option 4)
- Option 5)

In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes.
To be together again, the minute hand must gain 60 minutes over the hour
hand.
55 min. are gained in 60 min.
60 min is gained in (60/55) x 60 min =720/11 min.
But, they are together after 65 min.
Gain in 65 min =(720/11)-65 =5/11min.
Gain in 24 hours =(5/11 * (60*24)/65)min =1440/143
The clock...

The minute-hand of a clock overtakes the hour-hand at intervals of 65 minutes of the correct time. How much in a day does the clock gain or lose?

- Option 1)
- Option 2)
- Option 3)
- Option 4)
- Option 5)
None of these

For these kinds of problems, there is a direct formula
720/(11 - M) (24 x60/M) = Minutes
Where m = intervals of n minutes of the correct time,

A watch, which gains uniformly, was observed to be 4 minutes, slow at 6 a.m. on a Monday. On the subsequent Thursday at 7 p.m. it was noticed that the watch was 6 minutes fast. When did watch show the correct time?

- Option 1)
5 p.m. Tuesday

- Option 2)
4 p.m. Tuesday

- Option 3)
None of these

- Option 4)
3 p.m. Tuesday

- Option 5)
6 p.m. Tuesday

At 6 AM on Monday, the time is shown by the clock = 5: 56
At 7 PM on Thursday, the time shown by the clock = 7:06
Difference between the times in hours = 24 + 24 + 24 + 13 => 85 hours
In 85 Hours clock covered 10 Minutes.
To show the correct time it has to cover 4 Minutes,
Time is taken to gain 4 minutes = 4 x 85/10 => 34 Hours
The exact time when the clock will show correct time = Monday 6 AM...

At what time between 5 and 6 O'clock, will the hands of a clock be at an angle of 62°?

- Option 1)
5 hours

- Option 2)
5 hours

- Option 3)
5 hours 16 minutes

- Option 4)
Both (2) and (3)

- Option 5)
None of these

We know that In 60 Minutes,
Minute hand covers 360 degrees.
Hour hand covers 30 degrees.
In every 60 Min Minute hand covers 330 degrees more than the hour hand.
330 degree in minutes = 55 Minutes
So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.
To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11
Case 1 - When the minute hand is behind
The distance while...

What time does the clock show when the hour hand is between 3 and 4 and the angle between the two hands of the clock is 50°?

- Option 1)
min past 3

- Option 2)
min past 3

- Option 3)
min past 3

- Option 4)
None of these

- Option 5)
Both (1) and (2)

The angle between the two hands of a clock is 70°, when the hour hand is between 7 and 8. What time doest the watch show?

- Option 1)
7 hours

- Option 2)
7 hours

- Option 3)
7 hours

- Option 4)
Both (1) and (2)

- Option 5)
None of these

At what angle are the hands of a clock inclined at 20 minutes past 7?

- Option 1)
80°

- Option 2)
90°

- Option 3)
100°

- Option 4)
110°

- Option 5)
120°

Formula to calculate angle = (11m/2) - 30h
Where, m = minute & h = hour
So, Angle when the time is 20 Minute past 7 = (11 x 20/2) - 30 x 7 => 110 - 210 => -100
Ignore the negative sign.
Then, angle = 100

At what time between 3 and 4 O'clock are the hands of a clock in the opposite direction?

- Option 1)
3 hours

- Option 2)
3 hours

- Option 3)
3 hours

- Option 4)
none of these

- Option 5)
3 hours

We know that In 60 Minutes,
Minute hand covers 360 degrees.
Hour hand cover 30 degrees.
In every 60 Min Minute hand covers 330 degrees more than the hour hand.
330 degree in minutes = 55 Minutes
So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.
To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11
At 3 'o' clock,
The distance between the minute hand and hour...

At what time between 6 and 7 O'clock, are the hands of a clock together?

- Option 1)
6 hours

- Option 2)
6 hours 30 minutes

- Option 3)
6 hours

- Option 4)
6 hours

- Option 5)
6 hours

We know that In 60 Minutes,
Minute hand covers 360 degrees.
Hour hand cover 30 degrees.
In every 60 Min Minute hand covers 330 degrees more than the hour hand.
330 degree in minutes = 55 Minutes
So, we can conclude that in every 60 Minute Minute hand is 55 Minute ahead.
To be 1 minute ahead, time taken by minute hand = 60/55 = 12/11
At 6 'o' clock,
The distance between the minute hand and hour...

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

- Option 1)
120°

- Option 2)
125°

- Option 3)
130°

- Option 4)
140°

- Option 5)
135°

Formula to calculate angle = (11m/2) - 30h
Where, m = minute & h = hour
So, Angle when the time is 3:40 = (11 x 40/2) - 30 x 3
= 220 - 90 => 130 degree

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

- Option 1)
- Option 2)
- Option 3)
- Option 4)
- Option 5)

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

- Option 1)
320 degree

- Option 2)
135 degree

- Option 3)
155 degree

- Option 4)
none of these

- Option 5)
165 degree

Hour hand covers 30 degrees in 1 hour.
5 hours & 10 Min => 5(1/6) or 31/6 hours
Thus, the angle covered in 31/6 hours = 30 x 31/6 => 155 degree

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

- Option 1)
- Option 2)
- Option 3)
- Option 4)
- Option 5)

Formula to calculate angle = (11m/2) - 30h
Where, m = minute & h = hour
So, Angle when the time is 10:25 = (11 x 25/2) - 30 x 10
= 137.5 - 300 => 162.5
Reflex Angle = 360 - 162.5 => 197.5

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?

- Option 1)
144º

- Option 2)
150º

- Option 3)
140º

- Option 4)
180º

- Option 5)
168º

Hours between 8 AM to 2 PM => 6 Hours
6 Hours = 60 x 6 => 360 Minutes
In 360 Minutes, Angle covered by Hour Hand = 360 x 1/2 => 180 degree

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