Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.7)


At what time between 5.30 and 6 will the hands of a clock be at right angles?

43 5 min. past 5
43 7 min. past 5
[C]. 40 min. past 5
[D]. 45 min. past 5

Answer: Option B


At 5 o'clock, the hands are 25 min. spaces apart.

To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.

55 min. spaces are gained in 60 min.

40 min. spaces are gained in 60 x 40 min = 43 7 min.
55 11

Required time = 43 7 min. past 5.

Bala said: (Oct 9, 2010)  
How (25+15) is written? Plse explain it clearly.

Nitesh Nandwana said: (Oct 13, 2010)  

Bala it is very simple.

For right angle we need 90 degree between hour hand and minute hand.

So here we are looking for that condition.

Now look at hour hand on 5 o'clock, you'll get that minute hand should be at 5. 40 to form right angle.

(90 degree between hour and minute hand).

Now move minute hand to 25 min, now minute hand and hour hand are together (forms 0 degree).

Now simply move 15 min more to form right angle.

Don't think why it is "25+15", think we need 40 to form right angle, consider on logic instead of calculation.

Reddilavan said: (Oct 31, 2010)  
There is a formula for finding time nd degree
ie angle=(11/2)*min-30*hr
in this problem the hr nd min hands should be in right angle that means angle=90 then we can find min
=43 7/11 ie 5hrs 43 7/11min

Priya said: (Dec 14, 2010)  


Nagaraj said: (Dec 18, 2010)  
@red:how u got tis formula!!!

Prasad said: (Jan 5, 2011)  

The formula you provided is Master formula. It works on almost all kind of problems of clock to find angle between the clock hands. Just take care of angle while choosing.

Abhishek said: (Jan 13, 2011)  
It seriously a gud formula... we would be obligeed if we have more such formulae from your end.

Chandra Shekar said: (Feb 7, 2011)  
How did you get the fraction 60/55 in the above the calculation ?

Shree said: (Feb 13, 2011)  
Hey in some prob we are using theta=30h-11m/2 and here reddilavan has mentioned theta=11m/2-30h. How we knew in which prob which formula must be used na? Can any one explain me.

Akki said: (Apr 3, 2011)  
@Reddilavan how you got 90degree angle

Madhu said: (Jul 21, 2011)  
A right angle is an angle that bisects the angle formed by two halves of a straight line is called right angle and the angle between the two halves is 90 degrees. In the given problem handles of clock are in right angle so we take 90 degrees angle.

Siri said: (Aug 17, 2011)  
Acc to formula in 60 min we gain 55 spaces

So, for 1min = ?
60min=55 gains
so by cross multiplicatn
we get

Abhiram said: (Oct 1, 2011)  
@Akki, The given question is hands must be in right angles so 90 degrees is taken.

@Shree, You can take any f the formula but take care not to get a -ve theta if it comes -ve then take another formula ts as simple as such.

Deepika said: (Jan 15, 2012)  
There is a direct formula for it...
30xH + 11/2xM where H is for hours and M is minutes..

for e.g. in 4.20 pm....
H= 4
M= 20

Naresh said: (Jan 24, 2012)  

You are great

Dinesh said: (Feb 3, 2012)  
Thank you Reddilavan.

Ajay said: (Aug 25, 2012)  
Yes @shree I have same prob that how we use theta value.

Palikila Sridevi said: (Sep 6, 2012)  
Please explain me briefly how.

"55 min. Spaces are gained in 60 min" came.

Vip said: (Sep 16, 2012)  
Thanks! abhiram.

Susmitha said: (Oct 9, 2012)  
In 1 hour a minute hand covers 60 minute divisions (minute spaces) where as an hour hand covers only 5 minute divisions in 1 hour. Thus minute hand gains 55 (i. e;60-5) minute divisions in 60 minutes (1 hour).

Arjun said: (Dec 14, 2012)  
What is right angle?

Harry said: (Dec 21, 2012)  
@Reddilavan Can you please explain how to decide the exact formula

1) angle=(11/2)*min-30*hr
2) angle=30*hr-(11/2)*min

Which formula is correct ?

Amit said: (May 16, 2013)  

Both the formulas are correct.

1st one is used for finding the angle when hour is less than 6.

2nd one is used when the hour is more than 6.

Pavansairam said: (Jun 28, 2013)  
If theta = 90 and you go for 1st(b/w 5.30 to 6.00 etc problems).

If theta = 180 you go for 2nd.

Shubham said: (Jul 20, 2013)  
Can any one let me know that the angle which we always consider is in clockwise direction or we can consider that in anticlockwise direction too.

Chan said: (Jul 27, 2013)  

If the hour is equal to 6, then what is the formula for that.

Is it the angle 180 for straight angle and 90 for right angle.

Margaret said: (Aug 31, 2013)  
If we consider the basic solution, and start at 5:30 then min. space between hands at that time is 5 spaces and we need 10 more spaces to get right angle.

So simply (60*10)/55 min past 5:30 i.e. 30 min.+(60*10)/55 min. past 5.

What is wrong in the solution?

Prithish said: (Oct 23, 2013)  
Instead of only taking 25+15 we can also take 25-15, that will also be a right angle.

Priya said: (Feb 11, 2014)  
Why you are consider 5 while given time is 5:30?

Vaibhav Patil Jadhav said: (Mar 13, 2014)  
If the hours are less than 6 or the angle less than 180 then use...theta =11/2(min)-30(hrs).

If the hours are greater than 6 or the angle greater than or equal to 180 then use...theta = 30(hrs)-11/2(min).

It's simple and helps a lot. Good luck.

Vaibhav Patil Jadhav said: (Mar 13, 2014)  

We can't write 5:30 as (5+1/2)hrs bcoz it is written 5 hrs from 5 to 6 o'clock....we automatically find the minutes where they both meet using the formula theta = 11/2(min)-30(hrs) as the angle is less than 180.

Vaibhav Patil Jadhav said: (Mar 13, 2014)  
Hi guys,

Here either of the formulas can be applied but the thing is the angle must not be negative you definitely gets the answer.

Theta = 11/2(min)-30(hrs)...or theta = 30(hrs)-11/2(min).

Good luck.

Jeyamani said: (Jul 21, 2014)  
Actually the question is between 5.30 & 6.00. But you have taken from 5.00. Why?

Ramkant said: (Sep 28, 2014)  
Why the 15 min extra is added?

Akshi Panwar said: (Oct 9, 2014)  
15 minutes is added because perpendicular in clock is at 15 min.

After every 15 min gap between hour hand and min hand there will be a 90 degree angle is formed.

Modon said: (Nov 24, 2014)  
@Chandra Shekar.

At 12 pm both hour and second hands are in the same line. If it is 1 pm the hour hand is at 1 and minute hand at 12. So difference is 5 mins.

We can say, reach 1 from 12 (hour hand) needs 60 mins but space difference is 5 mins. So in 60 mins 55 mins space covered.

Aaaa said: (Dec 12, 2014)  
If 40 past 5 makes 90 degrees why isn't that the answer?

A V said: (Jan 13, 2015)  

Because hour hand will move too as 40 mins passes by. Thereby, no chance to get an exact 90 ° formation between hands.

Jonas Palmiano said: (Feb 10, 2015)  
What time after 4 o'clock will the hands of the clock be at right angle? Please help.

Ranjeesh said: (May 25, 2015)  
@Reddilavan your formula is ok. But why are you take only the number 5 in our west. Time give 5.30. Any one can explain?

Krish said: (Aug 5, 2015)  
I have the same doubt as @Margaret said. Please anyone explain it.

Nagu said: (Sep 14, 2015)  
Why the spaces are same for 5'clock and 7'clock == 25 spaces?

In which direction we have to take the spaces clock wise or anti clock wise?

Abc said: (Sep 24, 2015)  
Superb formula. Thanks alot.

Adi said: (Nov 26, 2015)  
Dear sir,

Please prove formula.

Prashanth said: (Dec 13, 2015)  
If the minute hand is present before hour hand then use theta = 11/2min-30hr.

Like that hour hand is before minute hand theta = 30hr-11/2hr.

Use it you will get exact solution.

Lakhan Singh Meena said: (Feb 27, 2016)  
Direct formula:

6*x - 90 = 30(y + x/60);

Where y = 5 hr.

So 6x = 30(5 + x/60) + 90;

x = 43(7/11)min. past 5.

Tilak Dewangan said: (Mar 23, 2016)  
Sorry @Riddilavan your formula may wrong if you solve this question.

How many minutes after 7 o'clock and before 8'o clock will the hands of the clock be in opposite direction?

Prithvi said: (Jun 13, 2016)  
Thanks @Harry.

Kumar said: (Aug 3, 2016)  
Since for 1 hour, the minute's arm move 360 degrees. And for each hour arm move 30 degrees.

Hence for every 1 degree move the minute's arm move 12 degrees.

When the time is 5 : 30 the angle between the min arm and hour arm is 15 degree.

Our target to find a time when the angle is 90 degree.

For this, we solve the equation :12x - x + 15 = 90.

From here we get x = 75/11.

30 degree = 1 hour.

75/11 degree = 1/30 * 75/11 = 5/22hours = 300/22min.

Hence final time is 30 + 300/22 = 480/22 min from 5 o'clock. (we add 30 because we have considered the arms move from 5:30).

Mounika said: (Aug 26, 2016)  
I was getting confused in using the formula.

But your answer helps me, Thankyou @Prashanth.

Yuvrajsinh said: (Sep 12, 2016)  
Friends please help me, I don't know this chapter.

Math Expert said: (Nov 4, 2016)  

Guess P = ANS .
(11/2) x (minutes) - 30 x (Hours) = 90 degree.
11/2 x P - 30 x 5 = 90,

P = 480/11= ANS.

Ashu said: (Mar 8, 2017)  
How can you get 11/2 in the formula?

Can anyone help me? Please.

Arpita Saxena said: (Apr 29, 2017)  
I didn"t understand this solution. Can anyone please explain?

Jeet said: (May 8, 2017)  
At 5.30, Angle between hands is 15 degree and 75' more required to make a right angle. Relative angle made by hands is 11/2 ' in a minute.

We can assume in x min they cover remaining 75.
So 11/2 * x = 75.
x = 150/11 min.
So at 30 + 150/11 min, they make a right angle.

Appu said: (Aug 16, 2017)  
At 5:30, the hands are 55 mins apart.To get an angle 90 btw them space must 15 mins apart,

so, the space is 55-15=40.
therefore,60/55-40=43 7/11.

A. M. said: (Sep 4, 2017)  
The given explanation doesn't consider the movement of the hour hand. Between 5:30 and 6, the hour hand will also have moved. Then the minute hand will need to cover a little more than (25 + 15) minutes' space.

Jack84 said: (Sep 26, 2017)  

AOB=25 min apart
To get 90 degree= minutes has to travel another 15 min from 5 O'clock i.e. 5:40 so, 25+15=40 min.
OB i.e.hour hand travels only 5 min in 60 min so=60-5=55 min,
the rest is given by experts.

Vijaya said: (Dec 14, 2017)  
I don't understand how, 15 m gain? please anyone explain it.

Saravana said: (Feb 22, 2018)  
How the calculation (60\55)*40 = 43*7/11?

Siddharth Pandey said: (Mar 12, 2018)  
Tell me both the times at which der will be 90-degree b/w min hand and second hand between 1 AM/PM to 2 AM/PM using the formula mentioned above. Does this formula work for given timings?

Saidul said: (Aug 1, 2018)  
Thanks @Harry.

Ragav said: (Oct 10, 2018)  
Why we can't use 30H - 5.5H = 90 formula?

30(11/2) - 5.5H = 90.

Sonam said: (Jan 23, 2019)  
Can you explain me the calculation of 43 7/11 min how it comes from (60/55*40) min?

Dipankar Mondal said: (Apr 26, 2019)  
40 * 12/11 = 43 7/11.

Swathi Sayyapureddy said: (Aug 25, 2019)  

When hour hand is preceding minute hand then theta=30H~11M/2 will be used otherwise, means when min hand is preceding hour hand then theta=11M/2~30H can be used.

Ajay said: (Dec 24, 2019)  
Thank @Ajay.

Abi said: (Jun 5, 2020)  
55min spaces are gained in 60min. What it is, Can someone explain to me this?

Babu said: (Jun 15, 2020)  
55min spaces are gained in 60min. What it is, Can someone explain to me?

Diksha Mishra said: (Aug 19, 2020)  
Please, someone, share the solution of how come40*60÷55 = 7÷11 came ? Pls someone explain it..

Ankita said: (Sep 2, 2020)  
@Abi and @ Babu.

When two hands coincide after exactly one hour, minutes hand travels one full circle that is 60 spaces but hours hand moves 5 space forward. So after exactly one hour later, they gain 55 spaces are their relative gain.

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