This document contains information about clocks, including: 1. Questions about the number of times clock hands coincide or form angles within 12 hours. 2. Concepts of relative speed in clocks and how often the hands meet (65 5/11 minutes). 3. A word problem about a clock that loses or gains time based on the minute hand overtaking the hour hand. 4. Sections about finding angles or time given the other, including problems involving defective or misaligned clocks.

1. Alosies George
IIM Calcutta
director@georgeprep.com
+91- 8420330256
Clocks
1
www.georgeprep.com 9985372371

2. Clocks
 How many times do the two hands of the clock coincide in 12
hours?
11 times (where is it lost?)
 How many times do the two hands of the clock make a 180
degree between them in 12 hours?
11 times. (Where is it lost?)
 How many times do the two hands of a clock make right angles
between them in 12 hours?
22 times. (Where is it lost?)
2
www.georgeprep.com 9985372371

3. Clocks
◦ The concept of relative speed in clocks
◦ Both the hands of the clock are together after every 65 5/11
mins.
◦ The clock is running fast – if the hands of the clock meet in less
than 65 5/11 minutes
◦ The clock is running slow – if the hands of the clock meet in
more than 65 5/11 minutes
3
www.georgeprep.com 9985372371

4. Clocks
Minute hand of a clock overtakes the hour hand at the intervals of 63 min of the
correct time. How much does the clock lose or gain in a day?
1. 54 22/77 mins
2. 56 8/77 mins
3. 55 8/77 mins
4. 56 6/77 mins
Ans : Option 2
4
www.georgeprep.com 9985372371

5. Clocks
 Given: Angle To find: Time
 Given: Time To Find: Angle
 Defective clocks
 Miscellaneous
5
www.georgeprep.com 9985372371

6. Clocks
Given: Angle
To find: Time
 What time between 4am and 5am will the two hands of the clock coincide?
[4:21:49]
 For how many times between 4m and 5am do the two hands make an angle
of 54 degree between them? What is the time during those instances?
[ 4:12:00 and 4:31:38]
6
Between n AM and (n+1) AM, formation of x
degrees.
2(30n – x) = 11m [before crossing the hour hand]
2(30n + x) = 11m [after crossing the hour hand]
www.georgeprep.com 9985372371

7. Clocks
Given: Time
To find: Angle
 What is the angle between the two hands at 2:15 am?
[22.5 degrees]
 What is the angle between the two hands of the clock at 3:40pm?
[130 degrees]
Per Hour Per minute
Hour hand 30 degrees 0.5 degrees
Minute Hand 360 degrees 6 degrees
7
www.georgeprep.com 9985372371

8. Clocks- Defective clocks
Ans : Option 3
8
A watch which gains uniformly is 5 min slow at 8:ooAM on Sunday and is 5
min 48sec fast at 8:00PM on the following Sunday. When did it show the
correct time?
1. 7:20 PM Tuesday
2. 7:20 AM Thursday
3. 7:20 PM Wednesday
4. 7:20 PM Tuesday
www.georgeprep.com 9985372371

9. Clocks- Defective clocks
Ans : Option 2
Anjali sets her watch at 6:10 am on Sunday, which gains 12 minutes in a day.
On Wednesday if her watch shows 2:50pm. What is the correct time?
1. 1:50pm
2. 2:10pm
3. 2:30 pm
4. 3:30 pm
9
www.georgeprep.com 9985372371

10. Clocks - Miscellaneous
Exchange of position of the hands of a clock.
1. A starts sleeping between 1pm and 2pm and wakes up at sometime
between 2pm and 3pm and finds that the hands of the clock have
interchanged their positions. How long did he sleep?
Ans: 55 5/13 mins
2. 2pm-3pm and 5pm-6pm
Ans: 2 10/13 hours
3. 10-11am and 5-6pm
Ans: 443 1/13 mins
10
www.georgeprep.com 9985372371