Clocks & Time

We consider clock to be a 60 minute space. 

I. 1 minute space = 6° degrees.

II. 60 minute space = 360°

III. In one hour, minute hand moves 60 minutes spaces where hour hand moves 5. Hence In an hour, minute hand gain 55 minute space over hour hand.  

IV. In 1 minute, hour hand moves 0.5° and minute hand moves 6°. Hence in 1 minute, the minute hand gains 5.5° or 11/2 degrees over the hour hand.

V. The hour & the minute hand coincide every 720/11 minutes. 

Incorrect Clock :-

I. It is said to gain time (fast) if hour hand & minute hand coincide in less than 720/11 minutes.

II. It is said to lose time (slow) if hour hand & minute hand coincide in more than 720/11 minutes.

Q1. After 5 O' clock, at what time will the hour & minute hand of the clock coincide for the first time ? (Time in HH:MM:SS format)

(1) 05:22:16 (2) 05:24:27 (3) 05:27:16 (4) 05:27:27 (5) 05:28:27

Solution :- 

At five of clock distance between hour and & minute hand is 150°
Speed of hour hand is 0.5° per minute.
Speed of minute hand is 6° per minute. 
Relative speed of minute hand & hour hand - 6°- 0.5° = 5.5° per minute
Time taken to meet = 150 / 5.5 = 27.27 minutes = 27 minutes 16 seconds

Q2. What is smallest angle between the minute hand & hour hand at 10.30 ?
(1) 225° (2) 120° (3) 132° (4) 315° (5) 135°

Solution:-
At 10 O' clock distance will be 300°.
In next 30 minutes, minute hand will move 180°(6° per minute) & hour hand will move 15°(0.5° per minute) in clockwise direction. Angular distance between them will be 135° or 225°. Hence answer is 135°. Answer option 5.

Q3. Minute hand & hour hand coincided after 60 minutes. Which of the following options is true ?
(1) Clock is gaining time.
(2) Clock is losing time.
(3) Clock is neither losing nor gaining time.
(4) It will again coincide after 61 minutes.


Solution :- We know that clock is said to gain time (fast) if hour hand & minute hand coincide in less than 720/11 minutes. Hence option 1.


Q4. A watch was running 8 minutes behind time on Sunday noon on date X. It was running 13 minutes ahead of time on next Sunday noon. After how much time after noon on X the clock was showing correct time ?
(1) 24 hours (2)  32 hours (3)  64 hours (4)  76 hours (5)  108 hours

Solution:-
First Sunday Noon : - 8 minutes
Second Sunday Noon : + 13 minutes
Time to cover in week time(168 Hours) = 21 minutes.
Time to gain from first Sunday noon to show correct time = 8 minutes.
21 minutes gain takes 168 hours.
8 minute gain will take = 168 * 8 / 21 = 64 hours from first Sunday noon. Hence answer option 3. 
-------------------------------------------------------------------
Go back to concepts to learn more-> click here