Clocks
Description: When it comes to the topic 'Clocks' it comes under the category of Logical Reasoning. This topic can be learnt easily and help you gain marks easily in campus placement, various other entrance exams.
Basics:
- In general, the shape of a clock is in a circular shape whose circumference is divided into 60 equal parts, called "Minute Spaces".
- In a clock, we can find 2 hands:
- Hour Hand ( smaller one)
- Minute Hand( bigger one)
- The complete angle in a clock is 360 degree
- So, the minute hand takes 1 hour to complete 360 degrees and the Hour Hand takes 12 hours to complete 360 degrees.
For Minute Hand, 60 min for 360°
01 min for x° we get x=6°
For Hour Hand, 12 hour for 360°
(12*60 min) for 360°
01 min for x° we get x=1/2°
Therefore in 1 minute the Minute hand moves 6°, Hour hand moves 1/2°
- In 60 minutes, the minute hand gains 55 minutes on hour hand
- In 1 hour, the minute and hour hand meets/coincides 1 time
- In 12 hours, the minute and hour hand meets/coincides 11 times
- In 24 hours, the minute and hour hand meets/coincides 22 times
- In 1 hour, both hands make 180 degree (opposite to each other) 1 time
- In 12 hours, both hands make 180 degree (opposite to each other) 11 times
- In 24 hours, both hands make 180 degree (opposite to each other) 22 times
- In 1 hour, both hands make 90 degree (right angle to each other) 2 times
- In 12 hours, both hands make 90 degree (right angle to each other) 22 times
- In 24 hours, both hands make 90 degree (right angle to each other) 44 times
Points to be remembered:
1. The speed of Minute hand is 6 degrees/min
2. The speed of Hour hand is 1/2 degree/min
3. Relative speed between both hands is 5(1/2) degree/min
4. When two hands are at right angle, they are 15 minute spaces apart
5. When two hands make 180 degrees, they are 30 minute spaces apart
6. And all the cases based on number of time hands coincide are to be remembered.
Formulae:
1. The angle between two hands is θ=| 30(h) - (11/2)(m)| where h is Hour,
m is minutes, || is mod
2. Actual time + Mirror Time = 12 hours (in problems to be considered as 11:60)
3. Reflex Angle=360° - actual angle(θ)
4. Miscellaneous formulas are covered in the sample examples.
Sample Problems:
1. What is the angle between two hands of a clock at 4:20 PM?
Sol. Consider the formula, θ=| 30(h) - (11/2)(m)|
Here h is 4, m is 20 substituting these in the above equation we get,
θ= 10°
2. What is the reflex angle between two hands of a clock at 4:20 PM?
Sol. Find the value of θ using the formula then substitute it in the below-mentioned formula.
Consider the formula, Reflex Angle=360° - θ
3. At what time between 5 and 6’o clock the two hands of the clock will coincide?
Sol. Since it is given they coincide (θ= 0°)
Consider the formula, θ=| 30(h) - (11/2)(m)|
Here h is 5, m is x (unknown), θ= 0°
Since mod is used, we will have 2 cases
Case 1: 0°= +(30(5)- (11/2)(x))
X= 27(3/11) minutes
Case 2: 0°= -(30(5)- (11/2)(x))
X=27(3/11) minutes
(Values are same as we have 0 in LHS, therefore we can go for any 1 case when (coincides/meet) is given)
** If hands coincide θ=0°
If hands are in straight line θ=180°
If hands are at right angle θ=90°
4. What is the correct time of the clock if the two hands of a clock shows 4:25 in the mirror?
Sol. Consider the formula, Actual time + Mirror Time = 12 hours (11:60)
Here, Actual time=X, Mirror Time=4:25
X + 04:25= 11:60
X= 11:60 - 04:25
X=07:35
05. How many degrees will the minute hand move in the same time in hour hand moves by 20°?
Sol. We know, Hour hand moves 1/2° in 1 min therefore it moves 20° in 40 minutes (simply follow cross-multiplication)
So hour hand takes 40 minutes
We know, Minute hand moves 6° in 1 min therefore in 40 minutes it moves 240° (simply follow cross-multiplication)
6. What is the angle made by minute hand in 44 minutes?
Sol. For Minute hand, 1 min is 6°
44 min is x (unknown value) using cross multiplication,
x=264°
7. A clock strikes once at 1’ o clock, twice at 2’ o clock and so on… for 1 day find no. of times it strikes?
Sol.
Consider, 1-1 time,2-2 times,3-3 times………….12-12 times we get the sum as 78
Since it is given in a day, 2 complete rotations in clock
Consider 78*2 =156 times
8. If a clock takes 22s to strike 12, how much time will it take to strike 6?
Sol.
For 12 strikes no. of intervals is (12-1) 11
Time to hear each strike= 22/11 = 2 sec
To hear 6 strikes no. of intervals=5
Therefore, to hear 6 strikes, 5*2 = 10s
Hint for Quick Calculation:
Consider x/(n-1) = y, for z strikes time to hear= (z-1)*y
x is Given seconds value, n is strike value, y is the value we get (Time to hear each strike)
z is strike value for whom time is to be found
16min for x
Therefore by cross multiplication x= 14.6min (mostly options are given in mixed fraction so find the value in such way)
10. How much time does a watch loose per day, if its hands coincides every 64 minutes?
Sol. Consider the formula, x=((720/11)-m)*(60*(24/m)) ,
Where m is minutes here m=64 min
After Substitution, x=32(8/11) minutes
Note: While finding angle between hands if past is mentioned (for example:10 minutes past 5 then the time to be considered is 5:10 )
If you have any doubts you can ask us in the comment section or you can mail us your queries.
For more number of practise questions you can mail us.
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