Clock Aptitude Formula, Clock Problem Shortcuts and Tricks
Clock Important Questions  Page 2
Clock Video Lecture  Page 3
Clock: The Face or dial of a watch is a circle whose circumference is divided into 60 equal parts, called minute spaces. A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
Clock Important Formulas
 In 60 minutes, the minute hand gains 55 minutes on the hour hand
 In every hour, both the hands coincide once.
 The hands are in the same straight line when they are coincident or opposite to each other.
 When the two hands are at right angles, they are 15 minute spaces apart
 When the hand's are in opposite directions, they are 30 minute spaces apart
 Angle traced by hour hand in 12 hrs = 360°.
 Angle traced by minute hand in 60 min. = 360°.
 Too Fast and Too Slow: If a watch or a clock indicates 8.15, when the correct time , 8 is said to be 15 minutes too fast.
 On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.
Solved Examples for Clock Problem
Question  1: The angle between the minute hand and the hour hand of a clock when the time is 4 : 20
Solution: Angle traced by hour hand in
Angle traced by min. hand in 20 min. =
Required angle = (130  120)º = 10º.
Question  2: How many times are the hands of a clock at right angle in a day?
Solution: In 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
Question 3: How many times in a day, are the hands of a clock in straight line but opposite in direction?
Solution: The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o' clcok only).
So, in a day, the hands point in the opposite directions 22 times
Question  4: At what time between 9 and 10 o'clock will the hands of a watch be together?
Solution: To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces. 55 min. spaces gained in 60 min.
45 min. spaces are gained in min
The hands are together at min past 9
Important Questions from Previous Year Paper
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Question 1 of 20
1. Question
1 pointsAt what angle the hands of a clock are inclined at 15 minutes past 5 ?
Correct
Angle traced by hour hand in
Angle traced by min. hand in 15 min.
Required angle
Incorrect
Angle traced by hour hand in
Angle traced by min. hand in 15 min.
Required angle

Question 2 of 20
2. Question
1 pointsAt what line,in minutes,between 3 o'clock and 4 o'clock,both the needles will coincide each other ? (R.R.B.2002)
Correct
At 3 o"clock ,the minute hand is 15 min.spaces apart from the hour hand.To be coincident,it must gain 15 min.spaces. 55 min.are gained in 60 min.
15 min.are gained in
The hands are coincident at min.past 3.
Incorrect
At 3 o"clock ,the minute hand is 15 min.spaces apart from the hour hand.To be coincident,it must gain 15 min.spaces. 55 min.are gained in 60 min.
15 min.are gained in
The hands are coincident at min.past 3.

Question 3 of 20
3. Question
1 pointsAt what times between 9 and 10 o"clock will the hands of a watch be together ?
Correct
To be together between 9 and 10 o"clock,the minute hand has to gain 45 min.spaces.55 min.spaces gained in 60 min.
45 min.spaces are gained in .or
The hands are together at min past 9Incorrect
To be together between 9 and 10 o"clock,the minute hand has to gain 45 min.spaces.55 min.spaces gained in 60 min.
45 min.spaces are gained in .or
The hands are together at min past 9 
Question 4 of 20
4. Question
1 pointsAt what time between 7 and 8 o"clock will the hands of a clock be in the same straight line but,not together ? (A.A.O.exam.2003)
Correct
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock ,they are 25 min.spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min.spaces are gained in
Required time = min.past 7
Incorrect
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.
At 7 o'clock ,they are 25 min.spaces apart.
Minute hand will have to gain only 5 min. spaces.
55 min.spaces are gained in
Required time = min.past 7

Question 5 of 20
5. Question
1 pointsA watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min.48 sec.fast at 2 p.m. on Monday.When was it correct ?(R.R.B.2001)
Correct
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
The watch gain min . or min.in 170hrs
Now, min.are gained in 170hrs.
2 min. are gained in hrs=50hrs.
Watch is correct 2 days 2 hrs.after 12 p.m. on monday i.e.it will be correct at 2 p.m. on Wednesday.
Incorrect
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
The watch gain min . or min.in 170hrs
Now, min.are gained in 170hrs.
2 min. are gained in hrs=50hrs.
Watch is correct 2 days 2 hrs.after 12 p.m. on monday i.e.it will be correct at 2 p.m. on Wednesday.

Question 6 of 20
6. Question
1 pointsA watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o" clock ,the true time is :
Correct
Time from 7 a.m. to 4.15 p.m. =9 hrs 15 min.= hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock
hrs of this clock = hrs of the correct clock
hrs of this clock hrs of the correct clock
The correct time is 9 hrs after 7 a.m i.e 4 p.m
Incorrect
Time from 7 a.m. to 4.15 p.m. =9 hrs 15 min.= hrs.
3 min. 5 sec. of this clock = 3 min. of the correct clock
hrs of this clock = hrs of the correct clock
hrs of this clock hrs of the correct clock
The correct time is 9 hrs after 7 a.m i.e 4 p.m

Question 7 of 20
7. Question
1 pointsThe angle between the minute hand and the hour hand of a clock when the time is 8.30, is
Correct
Angle traced by hour hand in
Angle traced by min. hand in 30 min. = = 180.
Required angel =
Incorrect
Angle traced by hour hand in
Angle traced by min. hand in 30 min. = = 180.
Required angel =

Question 8 of 20
8. Question
1 pointsThe angle between the minute hand and the hour hand of a clock when the time is 4.20 is :
Correct
Angle traced by hour hand in
Angle traced by min. hand in 20 min.=
Required angle =
Incorrect
Angle traced by hour hand in
Angle traced by min. hand in 20 min.=
Required angle =

Question 9 of 20
9. Question
1 pointsAn accurate clock shows 6 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 4 o'clock in the afternoon?
Correct
Angle traced by the hour hand in 2 hours =
Incorrect
Angle traced by the hour hand in 2 hours =

Question 10 of 20
10. Question
1 pointsThe reflex angle between the hands of a clock at 10.25 :
Correct
Angle traced by hour hand in
Angle traced by minute hand in 25 min
Incorrect
Angle traced by hour hand in
Angle traced by minute hand in 25 min

Question 11 of 20
11. Question
1 pointsHow many times do the hands of a clock at right angle in a day ? (I.A.S.1997)
Correct
In 12 hours, they are at right angles 22 times
In 24 hours,they are at right angles 44 times.
Incorrect
In 12 hours, they are at right angles 22 times
In 24 hours,they are at right angles 44 times.

Question 12 of 20
12. Question
1 pointsHow many times in a day, are the hands of a clock in straight line but opposite in direction ? (R.R.B.2003)
Correct
The hands of a clock point in opposite directions (in the same straight line)11 times in every 12 hours (Because between 5 and 7 they point in opposite directions at 6 o'clock only).So, in a day, the hands point in the opposite directions 22 times.
Incorrect
The hands of a clock point in opposite directions (in the same straight line)11 times in every 12 hours (Because between 5 and 7 they point in opposite directions at 6 o'clock only).So, in a day, the hands point in the opposite directions 22 times.

Question 13 of 20
13. Question
1 pointsHow much does a watch lose per day, if its hands coincide every 64 minutes ?
Correct
55 min. spaces are covered in 60 min.
60 min.spaces are covered in
Loss in 64 min.=
Loss in 24 hrs=
Incorrect
55 min. spaces are covered in 60 min.
60 min.spaces are covered in
Loss in 64 min.=
Loss in 24 hrs=

Question 14 of 20
14. Question
1 pointsAt what time between 4 and 5 o" clock will the hands of a watch point in opposite directions ?
Correct
At 4 o" clock ,the hands of the watch are 20 min.spaces apart.
To be in opposite directions, they must be 30 min.spaces apart.
Minute hand will have to gain 50 min.spaces.
55 min.spaces are gained in 60 min.
50 min.spaces are gained in
Required time = min.past 4
Incorrect
At 4 o" clock ,the hands of the watch are 20 min.spaces apart.
To be in opposite directions, they must be 30 min.spaces apart.
Minute hand will have to gain 50 min.spaces.
55 min.spaces are gained in 60 min.
50 min.spaces are gained in
Required time = min.past 4

Question 15 of 20
15. Question
1 pointsAt what time between 5.30 and 6 will the hands of a clock be at right angles ?
Correct
At 5 o'clock,the hands are 25 min. spaces apart.
TO be at right angles and that too between 5.30 and 6 ,the minute hand has to gain (25+15)=40 min.spaces.
55 min. spaces are gained in 60 min.
40 min.spaces are gained in
Required time=
Incorrect
At 5 o'clock,the hands are 25 min. spaces apart.
TO be at right angles and that too between 5.30 and 6 ,the minute hand has to gain (25+15)=40 min.spaces.
55 min. spaces are gained in 60 min.
40 min.spaces are gained in
Required time=

Question 16 of 20
16. Question
1 pointsA clock is started at noon.by 10 minutes past 5,the hour hand has turned through:
Correct
Angle traced by hour hand in 12 hrs = 360
Angle traced by hour hand in 5 hrs 10 min.i.e.Incorrect
Angle traced by hour hand in 12 hrs = 360
Angle traced by hour hand in 5 hrs 10 min.i.e. 
Question 17 of 20
17. Question
1 pointsAn accurate clock shows 8 o"clock in the morning.Through how many degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon ? (I.A.S.2000)
Correct
Angle traced by hour hand in 6 hours =
Incorrect
Angle traced by hour hand in 6 hours =

Question 18 of 20
18. Question
1 pointsAt 3.40, the hour hand and the minute hand of a clock form an angle of :
Correct
Angle traced by hour hand in 6 hours = 360
Angle traced by hour hand in 12 hours =
Angle traced by minute hand in 60 min.=360
Angle traced by it in 40 min. =
Required angle (240110) = 130
Incorrect
Angle traced by hour hand in 6 hours = 360
Angle traced by hour hand in 12 hours =
Angle traced by minute hand in 60 min.=360
Angle traced by it in 40 min. =
Required angle (240110) = 130

Question 19 of 20
19. Question
1 pointsHow many times do the hands of a clock coincide in a day ?
Correct
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1,they coincide only one,i.e. at 12 o'clock).
The hands coincide 22 times in a day.Incorrect
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1,they coincide only one,i.e. at 12 o'clock).
The hands coincide 22 times in a day. 
Question 20 of 20
20. Question
1 pointsHow many times in a day, the hands of a clock are straight ?
Correct
In 12 hours, the hand coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Incorrect
In 12 hours, the hand coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Important Videos on Clock Problem
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Comment made by Rh karan on Oct 1st 2017 at 2:44 am:
I want problems related to gaining or losing of clock