Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.11)

11. 

How many times are the hands of a clock at right angle in a day?

[A]. 22
[B]. 24
[C]. 44
[D]. 48

Answer: Option C

Explanation:

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

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


Pradeep said: (Aug 6, 2010)  
How 22 times in 12 hr?

Rahul said: (Sep 10, 2010)  
It should be 48 times.

Because for 1 hour right angle will be 2 times.

Sundar said: (Oct 12, 2010)  
The answer is 44.

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.

Chandra said: (Nov 15, 2010)  
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?

Hetal Ladani said: (Dec 3, 2010)  
How 22 times in 12 hr?

Jimeet said: (Jan 11, 2011)  
@chandra....ur answer is 32 8/11 mins past 4....corect me if i m wrng

Shivakarthik said: (Feb 23, 2011)  
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.

Prashant Kumar said: (Mar 23, 2011)  
In 60 min. 55 mins are gained by minute hand i.e. in 1 hour, hour hand lags by 5 mins.
in 12 hrs. , hour hand lags by 12*5=60 mins. i.e. 1 hr.
and in 1 hr dere r 2 right angles
hence in 12 hrs. 2 right angles will be lost resulting 22 instead of 22 and hence 44 in 24 hrs.

Manish said: (Aug 12, 2011)  
@prashant:

When 55 minutes are gained by minute hand then after 1 hour hand should lag by 55 minutes and not 5 minutes

Balavignesh said: (Oct 7, 2011)  
@shiva karthik correct me if i am wrong. At 8oclock also the hands will be at right angle at 8 25 and 8 55. Thus it happens two times at 8 o clock also. so how it will be 22 times.

Pooja said: (Dec 4, 2011)  
In 1 hour 2 times right angles are formed so in 24 hour it will be 48 times formed but 2 will be common.

Shawisk said: (Jun 16, 2012)  
Yes right angel in 12 hours is 22 times.
Approximate time is.

00:15.
00:49.
01:20.
01:55.
02:25.
03:00.
03:30.
04:05.
04:40.
05:10.
05:45.
06:15.
06:50.
07:20.
07:55.
08:25.
09:00.
09:30.
10:05.
10:35.
11:10.
11:40.

Linda said: (Apr 4, 2013)  
Hey how many times do the clock hands form a 48 degree angle?

Babita Pandey said: (Jul 29, 2013)  
I think the true answer is 48 because the min and the hour hand make 2 right angles in 1 hour. According to this they both made 48 right angles in 24 hours.

Sanket said: (Aug 1, 2013)  
Hand of clock made 0 and 180 degrees 22 times in a day and every other degree 44 times.

Hari said: (Aug 16, 2013)  
Its not 8 o'clock and 2 o'clock its 1 o'clock and 2 o'clock that makes right angle one time. So it is 22 times for 12 hours. And 44 for 24 hours.

Bharathveer Reddy said: (Sep 26, 2013)  
Generally for every 1 hr at two points it makes right angles.

But between 2:00 to 4:00 we get 3 right angles (approx 2:25, 3:00, 3:30) instead of 4 times.

Similarly between 8 and 10.

So we get 22 for 12 hrs and 44 for 24 hrs.

Prashant Bhalani said: (Oct 12, 2013)  
We know very well that both hands meet 11 times in 12 hours and therefor 22 times in 24 hours.

Considering process of meeting,
Both hands will be at right angle for 2 times per meeting.

So 22*2 = 44 times..!!
Simple as that.

Ranjani said: (Feb 27, 2014)  
How the two hands are in right angle two times an hour? Kindly help me.

Naga Jyothi said: (Jul 12, 2014)  
For example let we consider 12 clock we have 2 right angles i.e. 12.15 and 12.45.

Tarun Parihar said: (Sep 11, 2014)  
3:00 and 9:00 are common so in 12 hours is 22 time or in 24 hours is 44 times.

Raju said: (Oct 15, 2014)  
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

Sonu Choudhary said: (Mar 4, 2015)  
If you switch to a rotating coordinate system in which the hour hand stands still, then the minute hand makes only 11 revolutions, and so it is at right angles with the hour hand 22 times.

In a 24 hour day you get 2*22 = 44.

Osh said: (Mar 10, 2015)  
How many times in a day do the hands of a clock form an angle of 45 degrees?

I know the answer is 44 times. But what is the reason?

Manjunathan said: (Apr 25, 2015)  
One full rotation not considered so 11*2*2 = 44.

Sanvi said: (Jun 13, 2015)  
How can it be 22? And more over even at 8 and 2'O clock right angles will occur.

Please give the exact explanation.

Shanmugam said: (Jul 7, 2015)  
How is answer come for 44?

Miss Clock said: (Sep 5, 2015)  
At 00.15 the minute hand has moved 90′ &the hour hand has also moved 7.5′. Thus they don't make a right angle.

Himanshu said: (Oct 4, 2015)  
@Shawisk. The question is absurd. Because even at 1:20, the hr hand will be slightly ahead of 1 while minute hand will be at 4. Therefore making an angle of less than 15. Kindly help.

Ram said: (Dec 1, 2015)  
How many right angles does the hour hand of a clock move, when it goes from 12 to 3?

Dipanshu said: (Feb 8, 2016)  
How can answer C is right?

Ravinder said: (Mar 13, 2016)  
Hey guy do not gossip its right in 1 hr have right angle position came 44 times in 24 hr.

Abhay Phatangare said: (Mar 26, 2016)  
How many times does right angle create in an hour?

Shuham Singh said: (Mar 29, 2016)  
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.

Vishal Gajera said: (Apr 5, 2016)  
How many time the hands of a clock are at right angle between 1pm to 10pm?

Leonard said: (Apr 29, 2016)  
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?

Rohit said: (Jun 19, 2016)  
How many times starting at 1:00pm would the minute and hour hands of a clock make an angle of 40 degrees with each other in the next 6 hours?

Can anyone answer this question?

Pete said: (Jul 20, 2016)  
Leonard: You need to start at 12.00, not 3.00, as a day starts at 12.00 - read the question :-)

Jazcee said: (Aug 4, 2016)  
Hey, guys, this might help. The 2nd right angle of 2'oclock will be 3'oclock already. Same as the 2nd right angle of 8'oclock. Therefore in 12 hours there's only 22 right angles.

Mshadab2340 said: (Aug 6, 2016)  
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.

Pakixa said: (Aug 14, 2016)  
If the time is 3:30 that the angle would be?

Aditi said: (Aug 21, 2016)  
Hi, how do you say that in 22 hrs meet 11 times? I got a doubt in that. Please help me.

Viki said: (Sep 28, 2016)  
If the time is 8 : 40 then angle between them is 20° but hour and minute angle will be on the same line it should be 0° how it is 20°?

Please anybody tell me the answer.

Shankar Phulia said: (Oct 10, 2016)  
Is 7:20 is 90 degree or not? Please clarify.

Lala said: (Oct 30, 2016)  
How many time in 1 hour?

Ankit said: (Nov 7, 2016)  
How many times starting at 1:00 pm would the minute and hour hands of a clock make an angle of 40° with each other in the next 6 hours?

Please tell me the answer.

Ankit said: (Nov 7, 2016)  
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.

Rahul said: (Dec 6, 2016)  
Thanks for the explanation @Sundar.

Lucy said: (Dec 14, 2016)  
If the time was between 10 and 11 am and the clock hands were 180 degrees apart what would the time be?

Buni said: (Dec 19, 2016)  
24 * (360-30)/360 = 22cyc ||in one cyc it formed twice right angle.
22cyc * 2 = 44.
Answer: 44 times.

Veronica said: (Jan 11, 2017)  
What angle do the clock hands make at 3:30?

Mayur said: (Jan 14, 2017)  
I got your answer. Thanks @Buni.

Indhuchoodan said: (Mar 11, 2017)  
I didn't understand the explanation. Can anyone help me?

Moatz said: (Apr 11, 2017)  
The number of degrees that the hour hand of a clock moves through between 1:00 PM to 3:30 PM in of the same day is?

Can anyone solve this.

Vasavi Reddy said: (Apr 26, 2017)  
I didn't understand this explanation please explain me clearly.

Naveen Kumar said: (May 24, 2017)  
At what point of the after 3 o'clock hour hand and the minute hand of a clock occur at right angle for the first time with the answer?

Please explain me.

Rasika said: (Jun 7, 2017)  
How many 90 degree angles between the hour hand and minute hand from 12 noon to 3 pm? How to calculate? please explain.

Shakil said: (Aug 6, 2017)  
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.

Niharika said: (Aug 21, 2017)  
What about the number of times 0 degrees comes in 12 hours (precisely 5am-5pm)?

Zips said: (Sep 3, 2017)  
How many times right angle is similar?

Vivaan said: (Sep 7, 2017)  
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.

Aditi said: (Dec 27, 2017)  
As for one hour right angle will be two times.

So, the answer is should be 48.

Pratik said: (May 4, 2018)  
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.

Deepanjan said: (May 31, 2018)  
How many times the two hands of a clock will make 180 degree from 4pm to 10pm?

Nishtha said: (Jun 10, 2018)  
How 22 right angles in 12 hours?

Darshan said: (Sep 20, 2018)  
Angle = (11*m)/2 - 30 * h.

Use this formula for solving the clock problem.

Mansi said: (Nov 13, 2018)  
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?

Vijay Kumar said: (Dec 3, 2018)  
The answer is 22 times.

Vivek S said: (Apr 27, 2019)  
The answer is 44.
In 1 hour= 2 times right angle.
But 3:00 and 9:00 is subtracted.

Gaurav said: (Dec 12, 2019)  
Finally, I agree with @Prashant Kumaar's explanation.

Shaikazharuddin said: (Nov 25, 2020)  
Thanks all for explaining.

Amcodes said: (Mar 31, 2021)  
=> 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.

Suvrat Advait said: (Apr 25, 2021)  
It's awesome. Thanks all for explaining.

Sathesh said: (Oct 26, 2021)  
At what time 90 degrees formed 11 and 12? Anyone, please explain.

Rahul said: (Jun 10, 2022)  
At 10 o clock, we can't observe a right angle. Right?

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