At what time between 3 PM to 4 PM minute hand and hour hand will be opposite to each other?

Correct Answer: 3 : 164/11

Explanation:

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

Correct Answer: 245°

Explanation:

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°

Correct Answer: 190°

Explanation:

At 1 : 40 from the formula here P = 1 and Q = 40 so required angle is 11 x 40/2 - 30 x 1 = 220 - 30 = 190 the required angle is 190°

Correct Answer: 10°

Explanation:

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°

Correct Answer: Friday

Explanation:

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

Correct Answer: None of these

Explanation:

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 Answer: 9 : 124/11

Explanation:

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

Correct Answer: 9 : 441/11

Explanation:

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 Answer: Saturday

Explanation:

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 Answer: Thursday

Explanation:

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.