At 3 O’clock, Minute hand is at 12 while the Hour hand is at 3. Again the minute hand has to sweep through ( 30 x 5 ) ie 150° for reaching the figure 5 to show 25 mins.
Simultaneously the Hour hand will also rotate for 25 mins. Thus starting from the mark, 3 the hour hand will cover an angle = (25 x 30) / 60 = 12.5°
Hence, Angle between Hour and the Minute hand = ( 60 – 12.5 ) = 47.5°
Workspace
A clock is set right at 5 a.m. The clock loses 16 min. in 24 hours. What will be the true time when the clock indicates 10 p.m. on the 4th day ?
Time from 5 a.m. on a day to 10 p.m. on 4th day is 89 hours.
Now, 23 hrs. 44 min. of this clock are the same as 24 hours of the correct clock.
i.e., ³⁵⁶⁄₁₅ hrs. of this clock = 24 hrs. of correct clock.
∴89 hrs. of this clock =hrs. of correct clock
= 90 hrs of correct clock.
So, the correct time is 11 p.m.
Workspace
A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is
To be together between 9 and 10 O’clock, the minute hand has to gain 45min.
spaces 55min. spaces are gained in 60min.
45min.spaces are gained in (60/55 × 45) min. or 49 1/11 min.
The hands are together at 49 1/11 min. past 9.
Workspace
A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
The speed of hour hand is 0.5 dpm (Degree per Minute)
And the speed of minute hand is 6 dpm.
So, 300 degree traverse by minute hand in 300/6 = 50 Minutes.
Thus, angle moved by the hour hand in 50 minutes is 50/0.5 = 25° degrees.
Workspace
The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of the correct time. How much the clock gain or lose in a day?
In 1 hour, the minute hand gains 330° over the hour hand. i.e. in 60 minutes, the minute hand gains 330° over the hour hand.
∴ In 16 minutes, the minute hand gains over the hour hand by
Workspace
How many times in a day, are the hands of a clock in straight line but opposite in direction?
The hands of a clock point in opposite directions (in the same straight line, making an angle 180° between them) 11 times in every 12 hours because between 5 and 7 they point in opposite directions at 6 ‘o clock only.
Hence the hands point in the opposite directions 22 times in a day.
This is already given as a formula and it’s is better to learn the answer by heart as 22 which can save time in competitive exams. (However, you should know the theory behind).
Workspace
How much does a watch lose per day, if its hands coincide every 64 minutes?
55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 × 60)min = 65 5/11 min
Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min
Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min
= 32 8/11 min
Workspace
The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
8 Seconds in 4 Minutes mean 120 Seconds (or 2 Minutes) in one hour.
From 4AM to 11PM (on the same day) = 19 hours
So, total seconds gain in 19 hours = 19 X 120 (Seconds gain per hour) = 2280 Seconds.
Now, 2280 Seconds = 38 Minutes (i.e. 2280/19 = 38)
Thus incorrect clock will show 11:38PM at 11PM.
Workspace
A clock which loses uniformly was observed to be 5 minutes fast at 4:00 p.m on a Friday. On the subsequent Sunday at 8:00 a.m, the watch was 3 minutes slow. When did the watch show the correct time?
Number of minutes lost = 8
Total time from 4:00 p.m. on Friday to 8:00 a.m. on
Sunday = 40 hours.
There for, It lost 8 minutes in 40 hours
Time taken to lose 5 minutes = ( 40 x 5) / 8= 25 hours.
Whenever it lost the first 5 minutes, the clock is going to show the correct time.
After 25 hours (i.e.,) at 5:00 p.m. on Saturday the cock shows the correct time
Workspace
The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
hrs. of correct clock
The hands coincide 22 times in a day.
