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
This being a leap year none of the next 3 year is a leap year. So, the day of the week will be 3 days beyond Monday i.e., it will be Thursday.
1600 years of 0 odd days and 30 years have 1 odd day. 49 years contain 12 leap years and 37 ordinary years and therefore (24 + 37) odd days i.e., 5 odd days i.e., 1949 years contain (0 + 1 + 5) = 6 odd days. 26 day of January contain 5 days.Total odd days = (6 + 5) = 11 or 4 days. So, the days was Thursday
1992 being a leap year, it has 2 odd days. So, the first day of the year 1993 will be two days beyond Wednesday i.e., it will be Friday.
The year 1979 being an ordinary year, it has 1 odd day. So, the day on 12th January, 1979
But January 12, 1980 being Saturday
? January 12, 1979 was Friday.
Counting the number of days after 3rd November, 1987 we have Nov., Dec., Jan., Feb., March., April.
So days = 27 + 31 + 31 + 29 + 31 + 4 = 153 days containing 6 odd days on 4th April, 1988.
So, the day was Tuesday.
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°
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 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
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
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°.
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