# Clock Problems

Clock Problems:-  The short trick of the clock,                         Part-I
concepts of clock

A.    Every Clock have three hands:-
1. Second hand,   2. Minute hand,   3. Hour hand
All problems in every competitive exam asked about only those of three hands.

B.    Formulae to find out
·     Normal Angle ( i.e. The angle between the minute  hand and hour hand of a clock )= 30H-11/2XM or 11/2XM-30H

(This formula is a universal formula to find out angle formed by hands of a  clock )
·
Reflex angle ( i.e. the angle between the minute hand and hour hand ) = 360–Normal angle.
·       ( Reflex angle is always greater than 1800 .)

C.    Short tricks to find out the angle between hands of a clock-

1.     If the ratio between the hour hand and the minute hand is 1:3 then angle=9M/2.
2.     If the ratio between the hour hand and the minute hand is 1:4 then angle=MX2
3.  If the ratio between the hour hand and the minute hand is 1:5or 1:6 then angle=M/2
4.     If the ratio between the hour hand and the minute hand is 1:8 then angle=(M-H)X2
5.     If the ratio between the hour hand and the minute hand is 1:10 then angle=5M/2
Where M→ Minute. H → Hour

6.     Angle trace/move/create by Minute hand in 1  minute= 60 .
15  minures =900
30 mimutes=1800
60   minutes=3600

7.       Angle trace /move/create by Hour hand in 60 mimutes=300
1 minute=  0.50

8.      Hands of Clocks become right angle (900 2 times in every 1 hour, that is in 1st  time and 2nd  time ( except  3 O’ Clock and 9 O’ Clock, in 3 & 9 o’clock they form only  1 time 900  ). i.e. in every 12 hrs right angle form 22 times and in 24 hrs right angle form 44 times.
D.    Coincides of hands of a Clock
v  Coincide or together or straight in the same direction:-

·        Normally, in every hour both minutes hand and hours hand clock, coincide one time but between 12 noon/ midnight and 1AM/PM  they never get together or coincide.

In every 12 hours hands of a clock coincides 11 times (except  12  to 1 hour).

In a complete day, there are 24 hours and so in 24hours hands of
a clock coincides total 22 times.

v Coincide or together or straight in opposite direction:-
·        In every hour both minutes hand and hours hand become straight 1 time in the opposite direction but from  6 o’clock to 7 o’ clock they never get straight in opposite direction.

So, in a complete day, ( in 24 hrs ) hands of a clock become straight in opposite direction 22 times.

How to find the angle between hands of a clock-

a.  1000           b. 200
c. 1360            d. 750

Trick Here H=8, M=30

Angle =30H-(11/2)xM    ( universal formula )    OR    Angle   = (11/2)x M-30H
= 30X8-(11/2)x30                                                              =(11/2)x 30-30x8
= 240-330/2                                                                        =330/2-240
=240-165                                                                            =165-240
=75                                                                                     =-750
* Both are same in degree measurement, i.e. 750 .   {i.e. + or-}

Q.2 What is the angle between hour hand and minute hand of a clock at 4: 30?
a. 800                   b. 1360
c.100                     d. 450

Trick   Here H=4, M=30

Angle =30H-(11/2)xM    ( universal formula)
=30x4-(11/2)x30
=120- 330/2
=120- 165
=450.

Q.3 What is the angle between the hands of a clock at 6: 18?
a. 900                   b. 320
c. 810                   d. 800

Trick   Here H=6, M=18

Angle =30H-(11/2)xM    ( universal formula)
=30x6-(11/2)x18
=180- 198/2
=180- 99
=810.
Short trick: Ratio of Hour hand and minute hand, H:M=6:18=1:3
Angle =9M/2=9x18/2=810.

Q.4   What is the angle between the hands of a clock at 3: 30?
a. 900             b. 320
c. 810             d. 750
Trick   Here H=3, M=30
Angle =30H-(11/2)xM    ( universal formula)
=30x3-(11/2)x30
=90- 330/2
=90- 165
=750.
Short trick: Ratio of Hour hand and minute hand, H:M=3:30=1:10
Angle =5M/2=5x30/2=750 .

Q.5 What is the angle between hour hand and minute hand of a clock at 9: 54?
a. 270                   b. 1360
c.1000                  d. 450

Trick   Here H=9, M=54

Angle =30H-(11/2)xM    ( universal formula)
=30x9-(11/2)x54
=270- 594/2
=270- 297
=-270.
= 270
Short trick: Ratio of Hour hand and minute hand, H:M=9:54=1:6

Q.6 What is the angle between hour hand and minute hand of a clock at 5: 25?
a. 270                   b. 1360
c.1000                  d. 450
Trick   Here H=5, M=25

Angle =30H-(11/2)xM    ( universal formula)
=30x5-(11/2)x25
=150- 275/2
=150- 137.5
= 12.50
Short trick: Ratio of Hour hand and minute hand, H:M=5:25=1:5
Angle =M/2=25/2=12.50 .

Reflex Angle Problems:-

Q.1 The reflex angle between hands of a clock at 6.30 will be-
a.450          b. 150
c.1790        d. 3450
Short trick: As we know the reflex angle is always greater than 1800. So, the answer will be d.3450 because all other option is less than 1800.
Or.
By formula-
Reflex angle = 3600- Normal angle                  Here H=6 ,M=30
= 3600- {30H-(11/2)xM}
=3600- {30x6-(11/2)x30}
=3600- {180- 330/2}
=3600- {180- 165}
=.3600- 150
=3450

Q.2 Find the reflex angle between hands of a clock at 7: 20?
a.330          b.254
c. 260         d. None

Trick Here H=7 ,M=30
Reflex angle  = 3600- Normal angle
= 3600- {30H-(11/2)xM}
=3600- {30x7-(11/2)x20}
=3600- {210- 220/2}
=3600- {210- 110}
=.3600- 1000
=2600.
Q.3 The reflex angle between hour hand and minute hand of a clock at 10:25 is-
a. 1800       b. 192½0
c. 1950       d. 197½0

Trick Here H=10 ,M=25
Reflex angle  = 3600- Normal angle
=3600- {30x10-(11/2)x25}
=3600- {300- 275/2}
=3600- {300- 137.5}
=3600- 162.50
=197.50
= 197½

Q.4 What angle is made by minute hand in 21 sec.?
a. 17000     b. 290
c. 2600       d. 2.10

Short trick: Angle made by minute  hand in S sec= (1/10) Xs
So, Angle made by minute hand in 21 sec = (1/10) x21
= 21/10
=  2.10
Q.5 What angle is made by minute hand in 90 sec.?
a. 90            b. 9.010
c.900           d. 2.10

Short trick: Angle made by minute  hand in S sec= (1/10) Xs
So, Angle made by minute hand in 90 sec = (1/10) x90
= 90/10
=90

Q.6 What angle is made by hour hand in 36 sec.?
a. 90            b. (3/10)0
c.900           d. 2.10
Short trick: Angle made by hour hand in S sec= (1/120) xS
So, Angle made by hour hand in 36 sec = (1/120) x36
= 36/120
= (3/10)0
Q.7 In a clock time shows 10: 30. Accordingly, the minute hand is at East, then in which direction is the hour hand?
a. North-West
b. South-East.
c. North- East.
d. South- West
d. Southwest.