Since, in a clock hour hand completes an angle of 360° in 12 h and there is a gap of 6 h between 8 am and 2 pm, so in 6 h, hour hand completes an angles of 180°.
There are 11 intervals when the clock strikes 12.
Time taken for 11 intervals = 48 s
? Time taken for 1 interval = (48/11)s
In order to strike 3, there are 2 intervals, for which the time taken = (48/11) x 2) = 88/11 s
Angle of 360° is covered by hour hand in 12 h .
So, angle of 135° is covered by hour hand in 12/360° x 135° = 4.5 h
Thus, required time = (3 + 4.5)h = 7.5 h = 7 : 30
Since, third Thursday is on 16th. So, for calculation of last day of the month, we should calculate the odd number of days, here total days are 15 till 31.
? Odd days = 15/7 = 1
? Day on last date of month = friday
That will be 5th Friday.
Angle traced by hour hand in 12 h = 360°
Angle traced by hour hand in 25/4 h = (360/12) x (25/4)° = 187.5°
Angle traced by minute hand in 60 min = 360°
Angle traced by it in 15 min = (360/60) x 15° = 90°
? Required angle = (187.5° - 90°) = 97.5°
Clock will make right angle at (5n + 15) x 12/11 min past n.
Given that, n = 3
? Clock will make right angle at ( 5 x 3 + 15 ) x 12/11 min past 3 . =30 x 12 / 11 min past 3.
= 328/11 min
So required time = 3 H 328/11 min
Three days earlier than Friday means Tuesday.
So, 7th day of month will be Tuesday.
14th day of month will be Tuesday.
19th day of month will be Sunday.
1st day of month is Monday.
6th day of month is Saturday.
13th day of month is second Saturday.
17th day is the fourth day after second Saturday.
The angle between hour hand and minute hand at 5 O'clock = 5 x 30° = 150°
Minute hand move in 10 min = 2 x 30° = 60°
Hour hand move in 10 min = 30°/6 = 5°
? Angle between hour hand and minute hand at 5 h 10 min = 150° - 60° + 5deg; = 95°
Director came at 12 : 15.
Steno came at 12 : 40.
Since, steno was late by 30 min to the meeting.
? Meeting time 12 : 10
Since, angle between two number is 360°/12 = 30°
When the time is 3:25 pm, the minute hand will be at 5 and will have moved 60° from 3 and hour hand would be between 3 and 4 it will move 30° in 60 min and so in 25 min it would have moved 30 x 25/60 = 12.5°
So, angle between two hand will be 60 - 12.5 = 47.5°
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