CLOCKS

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GETTING STARTED

☛ A clock has two hands – Minute hand and Hour Hand. The face of a clock is divided  into 60 parts- known as ‘minute spaces’. Every minute space corresponds to 6°.

☛ Minute hand (longer hand) starts from 12 and covers one full circle i.e. 360 ° in 1 hour

☛ The Hour hand starts at 12 and comes back to 12 (complete one full circle) in 12 hours

☛ In one hour (60 minutes), minute hand covers 360° whereas the hour hand covers only 30°

☛ In one minute, minute hand covers 6° whereas hour hand covers only 0.5°(Dividing 360° and 30° by 60 to get values for 1 minute)

Note: The above fact is important and will come in handy while solving questions

☛ In span of 60 minutes or 1 hour, minute hand covers 330° more than that of hour hand. Therefore, minute hand covers  5.5° more than that of hour hand

One of the most frequently asked question in clocks is:

 

Steps Involved: 

 1. Find angle traced by each – minute hand and hour hand

 2. Subtract smaller angle from larger angle

  • Finding the angle formed between two hands of the clock

Eg. Finding angle between hands of the clock at 2:55 PM

Step 1:

Angle traced by hour hand = Angle covered from 12:00 to 2:00 + Angle covered in 55 minutes (from 2:00 to 2:55)                                                         

= [2 x 30°+55 x 0.5°]

   ( Hour hand covers 0.5° in 1 minute)

= 87.5°

Angle traced by minute hand = Angle covered in 55 minutes from 2:00 to 2:55

 = [55 x 6°]

= 330°                                                     

Step 2:

Difference in angle = 330° – 87.5°

= 242.5°or 117.5°

NOTE:

In clock problems, an angle can be expressed in two ways :  x° or (360-x)°. The smaller of the two is considered as the angle and the larger one is known as the ‘reflex angle’. The angle between the two hands is therefore, 117.5°

Let us consider another example:

Eg. Finding angle between hands of the clock at 5:30 PM

Step 1:

Angle traced by hour hand  = Angle covered from 12:00 to 5:00 + Angle covered in 30 minutes (from 5:00 to 5:30)

        = [5 x 30° + 30 x 0.5°]

(Hour hand covers 0.5° in 1 minute)

                     = 16

Angle traced by minute hand = Angle covered in 30 minutes from 5:00 to 5:30

                  = [30 x 6°]

                  = 180°

Step 2:

Difference in angle = 180° – 165°

              = 15°or 345°. 

Thus, 15° is the angle between two hands and the reflex angle is 345°

Another type of question can be finding the time at which a particular angle is formed:

  • Finding the time when angle will be x°

CASE-I: Required angle less than angle at start of hour

Let us find the time when the angle between hands is 30° between 4 PM and 5 PM.  

Consider both the hands to runners in the clock. At 4 PM, the hour hand is leading by 120° whereas minute hand is at 0°. This is a circular track.

The angle between the hands will be 30° when:

CASE-II: Required angle more than angle at start of hour

Let us find the time when the angle between hands is 160° between 4 PM and 5 PM.

In previous example, required angle was less than the angle formed at the start of the hour. Here, 160° is more than 120°, angle at start of hour

The angle between the hands will be 160° when:

Therefore, if the x° is less than the angle formed by the hands at the start of the hour, use Case-I 

If x° is more than the angle formed by the hands at the start of the hour, use Case -II

  • Hands of clock forming  0°, 180° and 90° 

Number of times hour hand coincides with hour hand in a day = 22 times

Number of times hour hand is exactly opposite to hour hand in a day = 22 times

Number of times hour hand and minute hand are at 90° in a day = 44 times

The Detailed Explanation for above fact is:    DETAILED EXPLANATION_Clocks

PRACTICE PROBLEMS

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Clocks

1 / 41

A flight departs from Dallas,US to India on 4th Dec 11:00 PM(US time) and reaches India on 6th Dec 8:30 AM (Indian Standard Time). If Indian Time is ahead of the  Dallas time by 10 hrs 30 min, find the time duration of the flight.

2 / 41

The circular measure of the included angle formed by the hour hand and minute hand of a clock at 5 PM will be

3 / 41

What time does the mirror image of an analog clock at 4'O clock show?

4 / 41

At what time between 2 o'clock and 3 o'clock will the two hands of the clock be at the right angle to each other for the first time?

5 / 41

A clock gains 10 minutes per day. If it is set right at 12 noon, the time it shows at 6 AM  next day is

6 / 41

How many times in a day, are the hands of a clock in straight line but not opposite to each other?

7 / 41

A watch which gains uniformly is 4 minutes low at noon on Tuesday and is 5 min fast at 6 A.M. on the following Tuesday. When was it correct?

8 / 41

When the two hands are linearly opposite to each other, they are ---------- minute spaces apart,

9 / 41

What is the ratio of 15 minutes to one hour?

10 / 41

When the hands are at 42°,they are ------- minute spaces apart,

11 / 41

A clock is started at noon. By 20 minutes past 3, the hour hand has turned through

12 / 41

What time will it be 4 hours from now in India, if in the UK it is 2:15 AM?

Time is India is GMT + 05:30 whereas UK follows GMT.

13 / 41

A watch which gains uniformly is 1 minutes low at noon on Monday and is 3 min.48 sec fast at 12 p.m on the next day. When was it correct?

14 / 41

The angle between the minute hand and the hour hand of a clock when the time is 4:25 is

15 / 41

How many minutes approximately does a watch lose or gain per day, if its hands coincide every 63 minutes?

16 / 41

At 5:40 AM, the hour hand and the minute hand of a clock form an angle of:

17 / 41

At 7 o’clock, a clock ticks 7 times. The time between first and last ticks is 42 seconds. How long does it tick at 10′o clock ?

18 / 41

The angle between the minute hand and the hour hand of a clock when the time is 3:20, is:

19 / 41

In 20 minutes, how much more angle does a minute hand cover as compared to an hour hand?

20 / 41

How many degrees will the minute hand move, in the same time in which the second hand completes 25 rounds?

21 / 41

In every 60 minutes, the minute hand gains -------- minute spaces on the hour hand

22 / 41

An accurate clock shows 10 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 9 o'clock in the evening?

23 / 41

What is the angle made by the hour hand and the minute hand, if clock shows 3:50 pm ?

24 / 41

How many degrees will the hour hand move, in the same time in which the second hand covers 30 minute spaces?

25 / 41

At what time between 5 and 6 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions?

26 / 41

How many times do the hands of a clock form 60° in a day?

27 / 41

How many times do the hands of a clock form 80° in a day?

28 / 41

A watch which gains 75 seconds in 10 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated 4 o'clock, the true time is:

29 / 41

What time between 2 and 3 o'clock will the hands of a clock be at right angle?

30 / 41

At what time between 9 and 10 o'clock will the hands of a watch be in a straight line but not coincide?

31 / 41

How much does a watch lose or gain per day, if its hands coincide every 64 minutes?

32 / 41

The reflex angle between the hands of a clock at 8:20 is

33 / 41

The angle between the minute hand and the hour hand of a clock when the time is 4:30

34 / 41

At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line for the first time?

35 / 41

Find the angle between the hour hand and the minute hand of a clock when the time is 4:25

36 / 41

At what time between 3 and 4 o' clock are the hands of a 5 minutes apart for the first time?

37 / 41

A clock is set right at 8 a.m. The clock loses 16 minutes in 24 hours.What will be the true time when the clock indicates 1 a.m. on 5th day, assuming clock was set right on 1st day?

38 / 41

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

39 / 41

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

40 / 41

At what time, in minutes, between 1 o'clock and 2 o'clock, both the needles will coincide each other?

41 / 41

How many times do the hands of a clock form 30° with each other in a day?

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