# Aptitude - Clock - Discussion

Discussion Forum : Clock - General Questions (Q.No. 11)
11.
How many times are the hands of a clock at right angle in a day?
22
24
44
48
Explanation:

In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times.

Discussion:
76 comments Page 8 of 8.

@chandra....ur answer is 32 8/11 mins past 4....corect me if i m wrng

How 22 times in 12 hr?

At what time between 4 and 5'o clock will the 2 hands of a clock be
at an angle of 60 degrees with each other?

The minute hand moves 360 degrees in 60 minutes. This means that the angle of the minute hand is given by 6t, where t is number of minutes past midnight.

The hour hand moves 30 degrees in 60 minutes. This means that the angle of the minutes hand is given by 0.5t.

The hands start together at midnight. The first time they make a 90 degree angle is when the minute hand has moved 90 degrees further than the hour hand, so this is given by the equation:

6t = 0.5t + 90
5.5t = 90
t = 16 4/11

In other words about 16 minutes past midnight.

The next time is when the minutes hand has gained another 180 degrees on the hour hand, and is 90 degrees behind it:

6t = 0.5t + 270
5.5t = 270
t = 49 1/11

At about 11 minutes to 1 o'clock.

For every 180 degrees that the minute hand gains on the hour hand there will be one 90 degree angle, so every
49 1/11 - 16 4/11 = 32 8/11 minutes

24 hours is 1440 minutes.
1440 / (32 8/11) = 44.

So every 24 hours there are 44 right angles between minute hand and second hand.