Clock Questions Simplified – Solve in Less than 1 Minute – codewindow.in

/ Aptitude / By Coder_Shark

Various competitive examinations ask questions regularly based on Clocks. The clock is one of the most integral parts of our day-to-day life.
Assume you have an exam or you are going to watch a movie or cricket match everything happens and depends on the Clock.
If you don’t follow it, you will miss your bus, train, or flight or probably an academic year if you don’t reach on time.

Why are clock problems different?

We every time look at the clock to see what time it is, how much time we have before we leave home etc. However, we never come across problems in real life where someone asks us what is current angle in minute hand and hand hour hand? What will happen if your clock loses 5 minutes every hour.
Therefore, the way of us looking normally at the Clock is way different than what is asked in the exam.
Let us try to understand which things we should know before we actually solve problems on clocks.

Important formulae:

1) To find angle between minute and hour hand at any time (hh:mm)
30h – 5.5 m
h- hour in timing
m –minute s in timing
Post calculation ignore minus sign if it comes
2) Remember fraction 12/11

Types of Problems:

Angle Measurement in Clock:

Have look at the clock and try to remember minutes along with actual digits (1 to 12). When you see a circle you can easily remember it as 360 degrees.
We have 12 numbers and it is equally spaced (360/12 = 30 degrees).
The angle between each consecutive digit on the clock is 30 degrees.
We have 5 lines between 2 consecutive numbers and so 30/5=6 degrees.
The angle between each consecutive minute line is 6 degrees.

Type 1:

Question 1:

What will be the angle between minute and hr hand at 2:30?

Solution:

We have to remember simple formula whenever we have to calculate angle between the minute and hr hand
For hh:mm = 30h – 5.5m [where h is hours and m is minutes]
= 30h – 5.5m
= 30 * 2 – (5.5*30)
= 60 – 165
= -105 degrees
Ignore minus sign

The answer is 105 degrees.

Question 2:

What will be the angle between the minute and hr hand at 8:20?

Solution:

We have to remember the simple formula whenever we have to calculate the angle between the minute and hr hand.
For hh:mm = 30h – 5.5m [where h is hours and m is minutes]
= 30h – 5.5m
= 30 * 8 – (5.5 * 20)
= 240 – 110
= 130 degrees

The answer is 130 degrees.

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Type 2:

Question 1:

At what time between 4 to 5 minute and hour hand will coincide with each other?

Solution:

As we have to find between 4 and 5, imagine it is 4 o’clock time.
Let us make hour hand constant on 4.
In order to make minute and hour hand coincide minute hand has to travel from 12 to 4.
This is nothing but -> 4 * 5 = 20 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 20* 12/11
= 240/11
= 21(9/11) mins

The answer is 4 hr 21(9/11) mins.

Question 2:

At what time between 11 to 12 minute and hour hand will coincide each other?

Solution:

As we have to find between 11 and 12, imagine it is 11 o’clock time.
Let us make hour hand constant on 11.
In order to make minute and hour hand coincide minute hand has to travel from 12 to 11.
This is nothing but -> 11 * 5 = 55 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 55 * 12/11
= 5 * 12
= 60
= 11 hr + 60 mins
= 12 hr

The answer is 12 o’clock.

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Type 3:

Question 1:

At what time between 7 to 8 minute and hour hand will be in straight line but in opposite direction of each other?

Solution:

As we have to find between 7 and 8, imagine it is 7 o’clock time.
Let us make hour hand constant on 7.
In order to make minute and hour hand opposite of each other:
As hr hand is on 7 and to make in straight line and opposite we need to cover 180 degrees.
Opposite of 7 is 1
So minute hand has to travel from 12 to 1
This is nothing but -> 5 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 5 * 12/11
= 60/11
= 5(5/11) mins

The answer is 7 hr 5(5/11) mins.

Question 2:

At what time between 8 to 9, minute and hour hand will be in straight line but in opposite direction of each other?

Solution:

As we have to find between 8 and 9, imagine it is 8 o’clock time.
Let us make hour hand constant on 8.
In order to make minute and hour hand opposite of each other:
As hr hand is on 8 and to make in straight line and opposite we need to cover 180
degrees.
Opposite of 8 is 2.
So minute hand has to travel from 12 to 2
This is nothing but -> 2 * 5 = 10 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 10 * 12/11
= 120/11
= 10(10/11) mins

The answer is 8 hr 10(10/11) mins.

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Type 4:

Question 1:

At what time between 10 to 11, minute and hour hand will be in right angle?

Solution:

As we have to find between 10 and 11, imagine it is 10 o’clock time.
Let us make hour hand constant on 10.
In order to make minute and hour hand at right angle:
As hr hand is on 7 and to make in right angle it need to travel 90 degrees.
TO get 90 degrees to 10 we need to move 3 digits ahead that is 1
So minute hand has to travel from 12 to 1
This is nothing but -> 5 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 5 * 12/11
= 60/11
= 5(5/11) mins

The answer is 10 hr 5(5/11) mins.

Question 2:

At what time between 2 to 3, minute and hour hand will be in right angle?

Solution:

As we have to find between 2 and 3, imagine it is 2 o’clock time.
Let us make hour hand constant on 2.
In order to make minute and hour hand at right angle:
As hr hand is on 7 and to make in right angle it need to travel 90 degrees.
To get 90 degrees to 2 we need to move 3 digits ahead that is 5
So minute hand has to travel from 12 to 5
This is nothing but -> 5 * 5 = 25 minutes
Now recall fraction number 12/11 which will help to solve maximum clock problems
= 25 * 12/11
= 300/11
= 27(3/11) mins

The answer is 2 hr 27(3/11) mins.

Type 4:

Question 1:

How many times do hands (hour and minutes hand) of the clock coincide in a day?

Solution:

In 12 hours 11 times
11 to 1 – 1
1 to 2 – 1
2 to 3 – 1
3 to 4 – 1
4 to 5 – 1
5 to 6 – 1
6 to 7 – 1
7 to 8 – 1
8 to 9 – 1
9 to 10 – 1
10 to 11 – 1
In entire day 24 hrs : 22 times

The answer is 22 Times in a day hands of clock coincide.

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Question 2:

How many times do hands (hour and minutes hand) of clock are straight?

Solution:

Hands of clock coincides 22 times in day
[Note: Coincide 1 time between 11 to 1 and for rest 1 hr 1 time each]
Hands of clock are in opposite direction 22 times
[Note: Opposite in direction 1 time only between 5 to 7 and for rest 1 hr 1 time each]

The answer is 44 times in day hands of the clock are straight.

Question 3:

How many times do hands (hour and minutes hand) of clock are in right angle?

Solution:

[Note: In Right angle 1 time only between 8 to 10 and for rest 1 hr 1 time each]

The answer is 22 Times in a day hands of clock are in right angle.

Question 4:

How many times do hands (hour and minutes hand) of clock are straight line but opposite in direction?

Solution:

[Note: Opposite and straight 1 time only between 5 to 7 and for rest 1 hr 1 time each]

The answer is 22 times in day hands of clock are in straight and opposite direction.

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