# 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 1 of 8.

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.

Leonard said:   7 years ago
My answer contradicts nearly everyone! I make it 45 hits at 90 degrees separation in 24 hours.

Starting at 3.00 am we have our first hit. The second one occurs at just after 3.30 am because the hour hand has moved a little.

Repeating the process till we get to 9 are we end up with 12 hits in six hours.

The next hit is now hit 13, just after 9.30 am 11 more hits gets us back to 3.00 pm. 11 more back to 9 pm and a further 11 back to 3.00 am the next day. These add up to 45!

It is wrong to assume you just multiply the first 12 by 4 to get 48. In doing so you are counting 9am twice, 3pm twice 9pm twice thereby adding a further three on to the value of 45.

There is a flaw in the reasoning to get to 44, which seems to be the smart answer. I too tried it with a watch and verified 45 over and over.

Anyone agree with me?

Hi guys... Its simply only, for every 1 hr the min hand and the hour hand are right angles at 2 times so someone blindly calculate
24*2=48 actually its wrong ... at the time of 8 and 2 o clock the hands are right angles at 1 time 1y i.e right angle means both the hands have 15 min space, at the time of 8 & 2 both hands are right angles at 1 time only so 10*2=20 20+2=22

So in 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
try it with 1 time piece ... u will understand clearly.

Amcodes said:   2 years ago
=> 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.
(1)

Ankit said:   6 years ago
At one instant, the hour hand and the minute hand of a clock are one over the other in between the markings for 5 and 6 on the dial. At this instant, the tip of the minute hand
1. Is closer to the marking for 6.
2. Is equidistant from the markings for 5 and 6.
3. Is closer to marking for 5.
4. Is equidistant from the markings for 11 and 12.

I am giving SIMPLE EXPLANATION.

Yes, it's right that in each hour clock generally makes 2 right angles.

But between 2-4 it makes only 3 instead of 4 because, at 3 o clock, the right angle is common to both intervals of (2-3) and (3-4).

Similarly, 8-10 make 3 right angles.

ie, 22 right angles in 12 hours and 44 in a day.

Shakil said:   6 years ago
When time starts at 12 noon, at 12:15 angle b/w them is 90.

For 1 pm angle subtended by two hands as 90 degrees will twice. Once the minute hand is approaching the hour hand and once it is going away from hour hand. it is similar for 2 pm, but in the case of 3 pm only one time. for second chance it's out of range.

Vivaan said:   6 years ago
Yes, the answer is 44 times. In between 2-3 & 8-9 o'clock, only one 90° angle is formed. Hence, In 12 hrs. No of times 90° angles is formed decreases from 24 to 22. & In a day 44times, 90° angles is formed.

Fact: For any angle, the no of times it is formed in a day is 44 times.

Raju said:   8 years ago
Actually in general for every hour the right angle comes in two times.
So, the answer should be 2*12*2 = 48 times.

But the logical thing here is for 2 o clock and 3 o'clock, one right angle coincides,
Similarly for 8 and 9 o'clock another right angle coincides.

So, the final answer is 48-2 = 44

Shuham singh said:   7 years ago
Suppose you are starting counting number of right angles from midnight 12:00 clock.

Then in first 12 hours.

All hour makes a right angle 2 times except starting 12:00 clock and ending 11:00 clock only-only 1 time.

That's why in 12 hours it is 22 times. And in 24 hours it is 44 times.