## 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 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. 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 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 2nd June 2012 is Saturday then which day is 7th July 2012?

1. Number of days in June is 30 -2 = 28, and number of days in July is 7, total number of days is 28 + 7 = 35, when we divide 35 by 7 remainder is 0, or number of odd days is 0 hence 7th July must be the same day as that of 2nd June i.e. Saturday in this case.

##### Correct Option: D

Number of days in June is 30 -2 = 28, and number of days in July is 7, total number of days is 28 + 7 = 35, when we divide 35 by 7 remainder is 0, or number of odd days is 0 hence 7th July must be the same day as that of 2nd June i.e. Saturday in this case.