# Clock Questions : Logical Reasoning

In this post you will learn clock related questions which are asked in logical reasoning exams like GRE, GMAT, CAT, SSC, AFCAT, NDA, RRB, IBPS, SBI Po etc. All these questions are previously asked in the exams, hence they are extremely important to study.

## Concepts and Problems of Clocks

Before moving on to solve these questions, please remember the following formulas

### Concept of Mirror Image of Clocks

When clock is placed sideways to the mirror, there is a change in the position of the clock hands.

If you want to find the mirror image of the clock, use the following rule:
a. If the current time lies between 1:01 and 10:59
Then you have to subtract 11:60 to get the mirror image

b. If the current time lies between 11:01 to 1:00
then you have to subtract 23:60 to get the mirror image

Note: In mirrors, there is only sideways change in the object, the top and bottom remains the same.

### Concept of Water image for Clocks

When clock is placed above the water, there is change in top/bottom of the clock
Use the following rule to solve question

RULE
In order to find the clock water image just subtract 18:30/6:30/5:90 from the given time

### Q.1 What angle is made by second hand in 15 sec. ?

Sol. We know that,
Second hand does one complete revolution in 60 seconds
==> 60 seconds = 360 degree
==> 1 second = 360/60 degree
==> 1 second = 6 degree

Second hand makes 60 in 1 sec.

So,
It makes 15 X 60 in 15 sec.
That is 900 in 15 sec.

### (Q.2) What time is shown by the mirror if the real time is 9 : 27

For this type of question it is better to draw illustration for better understanding

Remember the two rules for Mirror Image of Clocks
a. If there is time between 1:01 and 10:59
Then you have to subtract 11:60 to get the mirror image

b. If the time lies between 11:01 to 1:00
then you have to subtract 23:60 to get the mirror image

In this question, time lies between 1 : 00 to 11 : 00
So we have to subtract 9 : 27 from 11 : 60
11 : 60 – 9 : 27 = 2 : 33
The mirror shows 2 : 33

Hence 2 : 33 is the right answer

### (Q.3) Time appears in the mirror 11 : 09. Then what time will be appear in clock?

The mirror time is 11 : 09, which lies between 11 : 00 to 1 : 00

So using the rule number (2), we have to subtract 11 : 09 from 23 : 60
==>23 : 60 – 11 : 09 = 12 : 51
==>The clock shows 12 : 51

Hence 12:51 is the right answer

### (04) The reflecting time is 3 : 43 then the real time of clock is ?

Sol. The reflecting time is 3 : 43 which lies between 1 : 00 to 11 : 00

So using the Rule (1) we have to subtract 3 : 43 from 11 : 60
==> 11 : 60 – 3 : 43 = 8 : 17
==> The real time is 8 : 17

### (05) Water image of clock is showing time 4 : 42 what is the real time

In this question, the case is different.
Earlier we were finding the mirror image of the clock, here we have to find the reflection image of clock from water. So we need to apply different rules here.

RULE
In order to find the clock water image just subtract 18:30/6:30/5:90 from the given time

So we have to subtract 4 : 42 from 6 : 30 / 5 : 90
==> 5 : 90 – 4 : 42 = 1 : 48
==> The real time is 1 : 48

### (06) What is the angle between minute and hour hand at 9 : 53 ?

If you want to find the angle between the minute and hour hand, please use the angle formula

Sol.  By angle formula
==> Angle = (M * 11/2)  – ( H * 30)
Where M is the minute value and,
H is the hour value

==>Putting the value of M and H in the above formula, M = 53 , H = 9

==> (53 X 11/2)  –  (9 X 30)
==> 291.50 – 2700 => 21.50

Hence 21.5 degree is the angle between the minute hand and hour hand

### (Q.7) What is the angle between minute and hour hand at 12 : 46 ?

Again using angle formula
==>Angle = (M * 11/2)  –  (H * 30)

Putting values of M & H where, M = 46 , H = 12
==> (12 * 30) – (46 * 11/2)
==> 3600 – 2530 = 1070

Hence 107 degree is the angle between the hour hand and minute hand

## (08) At what time between 10:00 to 11:00 o’ clock minute and hour clock coincide or make 0 degree?

For this type of question, we have to use following formula

Time => 2/11 * (A1 + A2) and 2/11 * (A1 – A2)
where,
==> A1 = 30 * Hour1
==> A2 = required hour and minute angle

In this question
=> A1 = 30 * 10 = 300
=> A2 = 0

Putting these values in formula
Time1 = 2/11 (300 + 0)=> 600/11
Time 2 = 2/11 (300 – 0)=> 600/11

600/11 can be written as 54.54 minutes

Hence the hour hand and minute hand coincide at 10:54 minutes

### (Q.9) At what time between 2 to 3 O’clock minute and hour hand will be at right angle to each other and makes 900 angle ?

For this type of question, we have to use following formula

Time => 2/11 * (A1 + A2) and 2/11 * (A1 – A2)
where,
==> A1 = 30 * Hour1
==> A2 = required hour and minute angle

In this question
=> A1 = 30 * 2 = 60
=> A2 = 90 degree

Putting these values in formula
Time1 = 2/11 (60 + 90)=> 300/11 => 27.27 minute
Time 2 = 2/11 (60 – 90)=> negative number so ignore

Hence hour hand and minute hand make 90 degree at 2 hour 27 minutes