Find the angle between minute hand and hour hand at 1 : 40 AM

At 4 : 20 A.M. from the formula here P = 4 and Q = 20 so required angle is 11 x 20/2 - 30 x 4 = 110 - 120 = - 10 or ignoring the negative sign the required angle is 10°

Three days after Saturday is Tuesday and Tuesday is a day before a day before yesterday So, yesterday is Tuesday.
Hence, today is Friday.

Next bus will leave at 9 : 35 am. So, last bus left at (9 : 35 - 0 : 30) = 9 : 50 am
So, inquiry clerk gave the information to the passenger at = (9 : 05 + 0 : 10)
= 9 : 15 am



So, the next Tuesday will come on the Mrs Susheela's wedding anniversary in 30th September, 2003

Total number of days from January 1 to march 1
     = 31 + 29 + 1
     = 61 days
(February in leap years = 29 days) = 61 ÷ 7
     = 8 weeks and 5 odd days
So, the fifth day from Friday = Tuesday

The century divisible by 400 is a leap year. The year 707 is not a leap year.

At 10 : 10 from the formula here P = 10 and Q = 10 so required angle is 11 x 10/2 - 30 x 10 = 55 - 300 = - 245 the required angle is 245°

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°.
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
They will be together when the minute hand will travel 90° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16 4/11 minute.
Hence they will coincide at 3 : 16 minute : 21.81 second

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°
Since relative speed between them is 11/2° per minute or every minute hand will travel 11/2° more than the hour hand.
Then will be opposite to each other when the minute hand will travel (90 + 180) = 270° more than the hour hand. And time taken for this is (270)/(11/2) = 540/11 or 49 1/11 minute
Hence they will be opposite to each other at 3 : 49 minute : 0.09 second

Consider exactly at 4 : 00, minute hand is at position '12' and hour hand is at '4' hence angle between these two hands at 4 : 00 is 120°
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
Then will be perpendicular to each other when the minute hand will travel (120 - 90) = 30° more than the hour hand. And time taken for this is (30)/(11/2) = 60/11 or 5 5/11 minute
Hence they will be perpendicular to each other at 4 : 11 minute : 45.45 second

Consider exactly at 9 : 00, minute hand is at position '12' and hour hand is at '9' hence angle between these two hands at 9 : 00 is 270°
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
Then will be together when the minute hand will travel (270 - 180) = 90° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16 4/11 minute
Hence they will be opposite to each other at 9 : 49 minute : 21.81 second