## Clock and calender

#### Clock and calender

1. At what time between 9 PM to 10 PM minute hand and hour hand will coincide ?

1. 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 hand will travel 11/2° more than the hour hand.
Then will be perpendicular to each other when the minute hand will travel 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 perpendicular to each other at 9 : 49 minute : 0.09 second

##### Correct Option: C

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 hand will travel 11/2° more than the hour hand.
Then will be perpendicular to each other when the minute hand will travel 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 perpendicular to each other at 9 : 49 minute : 0.09 second

1. If 14th October 2005 is Friday then which day is 14th October 2009?

1. Since in 1 year we have one odd day while in one leap year we have two odd days .
Number of odd days are: 1(for 2006) + 1(for 2007) + 2 (For leap year 2008) + 1 (for year 2009) so total number of odd days are 1 + 1 + 2 + 1 = 5 days. 5 days more than Friday means Wednesday.

##### Correct Option: B

Since in 1 year we have one odd day while in one leap year we have two odd days .
Number of odd days are: 1(for 2006) + 1(for 2007) + 2 (For leap year 2008) + 1 (for year 2009) so total number of odd days are 1 + 1 + 2 + 1 = 5 days. 5 days more than Friday means Wednesday.

1. If today is Monday then which day of the week is after 59 days.

1. Since a day of the week repeat after every 7 days, divide 59 by 7, remainder is 3 so number of odd days is 3, and 3 days after Monday is Thursday.

##### Correct Option: C

Since a day of the week repeat after every 7 days, divide 59 by 7, remainder is 3 so number of odd days is 3, and 3 days after Monday is Thursday.

1. If 14th October 2005 is Friday then which day is 14th October 2006?

1. Since in 1 year we have one odd day while in one leap year we have two odd days.
Number of odd days are 1 (for 2006)
1 days more than Friday means Saturday.

##### Correct Option: B

Since in 1 year we have one odd day while in one leap year we have two odd days.
Number of odd days are 1 (for 2006)
1 days more than Friday means Saturday.

1. At what time between 4 PM to 5 PM minute hand and hour will be at right angle to each other ?

1. 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

##### Correct Option: D

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