Aptitude - Clock - Discussion

=> 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.

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

Every hour, 2 right angles are formed between the hands. But because minute hand crosses hour hand every 55 mins, every hour, there is a 5-minute lag. For 24 hours, the lag is 24x5= 120 mins i.e. 2 hour lag - a loss of 4 right angles in 24 hours.

So: 24x2 - loss = 44.

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

A unique clock has 24 divisions instead of 12 nd functions like normal then how many times from noon will the hour and the minute hand form 90 degrees for the first time? Can anyone answer this?

The answer is 44.
In 1 hour= 2 times right angle.
But 3:00 and 9:00 is subtracted.

@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.

Why it's not 48? Please explain.

It's awesome. Thanks all for explaining.