Aptitude - Clock - Discussion

Thanks all for explaining.

=> When Hour and Min Hand are 15 mins and 45 mins away from each other, they form a right angle. So basically in every 60 min SPACES(not mins), they form right angles 2 times.

=> Let's start from 12 AM (0 degree angle).
55 min spaces are covered in 60 mins.
So 60 min spaces are covered in?
=(60*60)/55 mins.

> In a day there are 24 hours = 24 x 60 mins,
So how many such 60 min spaces exist in a day.
= ( (24*60) / ((60*60)/55)) = 22
So, 22*2 = 44 times they form a Right angle in a day.

It's awesome. Thanks all for explaining.

At what time 90 degrees formed 11 and 12? Anyone, please explain.

At 10 o clock, we can't observe a right angle. Right?

Simply speaking, every 15 min (4/Hour) is right angle except at 6 & 12, AM PM both. (24 x 4) - 4.

@All.

Since the clock coincides 22 times a day:

-> 55 minutes ahead (minute hand) in 1 hr.
Therefore, 60 minutes ahead will be in (1/55)*60 hr i.e 12/11 hr.
That means in 24 hrs minutes hand will be 60 minutes ahead 24/(12/11) times i.e 22 times.

-> Now After the minute hand coincides with the hour hand it makes 2 right angles with the hour hand before it is ahead of 55 minutes these 2 occur when the minute hand is 15, 45 minutes ahead of the hour hand (which is between 0 to 55)

-> Thereby between each coincidence they make 2 right angles so the total number of right angles = 22*2 = 44.

During 5:55pm and 5:55am, hour hand is inclined between 5 and 6 not in the straight line.

For 12 hours, 11 times.
For 22 hours, 22 times.

Why it's not 48? Please explain.

The hands of a clock are at right angles (90 degrees apart) 22 times in 12 hours.

This is because:

1. In one hour, the minute and hour hands are at right angles twice (except between 2:00 and 3:00, and between 8:00 and 9:00, where they are at right angles only once).

2. Therefore, in 12 hours, the calculation is:

- ( 2{ right angles/hour} times 10{ hours} = 20{right angles}).
- Plus the additional 2 occurrences from the remaining hours (once each in the intervals mentioned).

Thus, for a 24-hour day, the hands of a clock are at right angles:

22 {right angles (12-hour period)} x 2 = 44 right angles in a day.
So, the hands of a clock are at right angles 44 times in a day.