Aptitude - Clock - Discussion

Discussion :: Clock - General Questions (Q.No.3)

3. 

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

[A]. 145°
[B]. 150°
[C]. 155°
[D]. 160°

Answer: Option C

Explanation:

Angle traced by hour hand in 12 hrs = 360°.

Angle traced by hour hand in 5 hrs 10 min. i.e., 31 hrs = 360 x 31 ° = 155°.
6 12 6


Uma said: (Jul 1, 2010)  
I can't understand how that 31/6 come?

Pradeep Gorai said: (Jul 2, 2010)  
To Uma
5 hr 1o min=310min(5*60+10)
=310/60 hr
=31/6 hr.
or
5 hr 10 min=5+10/60
=31/6

Nilesh said: (Jul 3, 2010)  
I cant undrstand how that
31/6 hrs= (360/12 * 31/6) = 155

Pradeep said: (Jul 4, 2010)  
@nilesh
1hr=30 degree
.'. 31/6 hr= 31/6 * 30 =155 deg

Sandhya said: (Jul 28, 2010)  
5.10/60
=5.2/12
=5.1/6
=5*6+1/6
=31/6

Mariah said: (Oct 21, 2010)  
What is the formula of changing minutes or hours to degrees?

Nitin Harjai said: (Mar 21, 2011)  
I don't understand "by 10min past 5".

Akshay said: (Apr 3, 2011)  
10min past 5 is 5:10
so, 5+10/60 =5+1/6(cross multiply)=31/6

Naveed Mohammad said: (Jun 29, 2011)  
Formula for finding degree when min and hr ar given is

angle = (11/2)*m - 30*h when (11/2)*m > 30*hr
angle = 30*hr-(11/2)*m when (30hr > (11/2)*m

where m = min, hr = hours

=30*5-(11/2)*10
=150-(120/2)
=(300-120)/2
=180/2
=90 degrees

Its a time institute materiel solution.

Resham said: (Aug 10, 2011)  
Initially both hands are at 12(noon)
1 hr= 30 dgrs ( 12 to 5 = 5 hrs)
so 5*30 = 150 dgrs and
in 60 mins cover 30 dgrs
in 10 mins= 30/60
in 1 min= 30/60*10= 5 dgrs
so
150 + 5 = 155 dgrs

Narendran, S S said: (Aug 13, 2011)  
Angle between hr and min is given by

A =30*hr~(11/2)*min
= 30*5 - (11/2)*10
= 95 degrees

Now the angle swiped by the min hand alone is

6 degrees per min
hence 60 degrees per 10 min

Angle swiped by hr hand alone is
A+60 = 95+60 = 155 degrees.

Navaneetha Krishnan said: (Aug 28, 2011)  
Sir i can't understand that 155 degree for which timing?

Vinay said: (Aug 29, 2011)  
It is for 5 hours 10 minutes from noon (12).

Shravan Purohit said: (Sep 8, 2011)  
@navaneetha

Given : our hour hand started at noon i.e. 12 o'clock
and 10 minutes past 5 i.e. 5 hour 10 minutes
we find angle between 12 and 5.10 o'clock
firstly we convert 5hour 10min into minitus 5*60+10=310min
and 310min convert into hour 310/60=31/6

In 12h = 360
So in 31/6 h= (360/12)(31/6)=155 degree.

Kranti said: (Dec 7, 2011)  
Very nice explanatoin given by shravan.

Madesh said: (Jan 4, 2012)  
Don't worry I will explain Clearly....

Past 5 means 5 hours.. and 10 mins out of 60 mins.. that's (10/60)

So.. 5hrs + 10 mins= 5+(10/60) = 5+(1/6).. so. 6*5+1= 31/6hrs..

1hr= 30 degree... so 5hrs= 150 degree and that past 5(means 5degree)...

So 150+5 = 155.

Leenus said: (Jan 23, 2012)  
I can't understand "by 10 mins past 5".

Sasidhar said: (Feb 14, 2012)  
Here angle In 12h is = 360 degree
angle in 10 PAST 5 means 5:10

h=5, m=10

Now

|30h-11/2m|= degree
|30*5-11/2*10| = 95 degree

Now degree=360-95=155 degree. Got it friends?

Mary said: (Feb 25, 2012)  
Its easy
1hr=30 degree
ie 5hr=5*30=150 degree
also
10 min=10/60hr=1/6hr
we know 1hr=30 degree
ie
(1/6)*30=5 degree
so 150 deg+5 deg=155 deg.
its solved :)

Sowmya said: (Apr 28, 2012)  
How can it be 360-95=155? it is 265. I don't understand the logic.

Rupa said: (Aug 14, 2012)  
If 1hr=30degrees.

Then 5hrs= (5*30) =150degrees.

And then 10min= (10/60) =1/6.

1/6*30=5degrees.

The total is 155degrees.

Guru Govind said: (Aug 26, 2012)  
The question asked is not for angle b/w hours hand and minutes hand.the question is:how much distance only hours hand rotated from noon...
from 12 to 5:00 the hours hand rotated is 150degree.use the formula 30h-(11/2)*m=theta; now how much is the hours hand rotated in in 10min. i.e..for 1hour..it will make 30degree...for 10min..it will make 5degree. therefore 150+5=155

Yasin said: (Sep 9, 2012)  
5.10?
hour hand moves 30 degree's for 1 hour

for 5 hours 5*30

in 10 min 10\60*30(in min)

150+5=155

Santthosh said: (Jan 3, 2013)  
I accept all of your comments, but what my doubt is if minute hand makes 5 ticks of 6 degree to contribute 5 minutes, then hour hand is making 6 ticks of 5 degree to contribute 1 hour. Why this variations in the ticks?

Riyaz said: (Sep 14, 2013)  
A simple process is available Here:

Angle made by hour hand in one hour = 30 degrees.

By 5 hours = 5*30=150 deg.

Angle made by hour hand in one minute= 0.5 degrees.

For 10 min = 10*0.5 = 5 degrees.

Total angle made by Hour hand = 150+5 = 155 degrees.

Gyanendra said: (Dec 31, 2013)  
I agree with @Riyaz.

The simplest way:

i.e 1 min space = 6 degree.
And in 1min hr hand travel 1/2 degree.

5*5*6 = 150 degree.
10*(1/2)degree = 5 degree.

Total = 155 degree.

Thongoc992 said: (Mar 13, 2014)  
Hello. When I read this question and I drew 5.10 in the paper. I thought that we have to find the angle between minute hand and hour hand that makes 5.10, therefore I found out the answer was 90 degrees.

But the problem is I don't understand " a clock is started at noon". What does it mean? Could you guys explain for me, please!

Goutam Pramanik said: (Mar 16, 2014)  
Angle = 60*h-11*m/2.

Where, h=hour, m=minute.

John said: (Apr 23, 2014)  
@Shravan Purohit's explanation is superb. I found it difficult understanding it initially but after @Shravan's explanation, I now understand it perfectly. Thanks Shravan.

Bilal said: (Oct 6, 2014)  
Very simple we know that an hour hand covers 30' when moving from one number to next as total circle has 360/12 so 5 hour means it has covered an angle of 150' the rest 10 min should be converted first into hour as 10/60 and then multiplied with the same 30' to get 5. Now add 150+5 and you will get 155.

Abina said: (Oct 12, 2014)  
It is very simple, the question is 5hrs and 10 mns. They are asking short hand. So,
In short hand 1 min = 1/2 degree.

1 hr = 60min/2 = 30.
5hr = 5*30 = 150.
1 min = 10/2 = 5.

= 150+5 = 155 degree.
Answer : 155 degree.

Sagar Biswas said: (Feb 10, 2015)  
Nice solution I appreciate.

Jatinder said: (May 18, 2015)  
In 1 min hour hand = 1/2 degree /min.

For 10 min = 10*(1/2) = 5 degree.

In 1 hr hour hand takes 30 degree.

For 5 hr = 5*30 = 150.

And total angle traveled by hr hand = 150+5 = 155 degree.

Shiv said: (Jul 11, 2015)  
@Shravan Sir your explanation is mind blowing.

Sarawar said: (Sep 1, 2015)  
At n'o clock the angle of hour hand from vertical is 30 n; speed of hour hand is 5 degree per minute; speed of minute hand is 6 dpm.

At 5.10 angle of hour hand from vertical 5*30+0.5*10 = 155 degree.

Angle of minute hand from vertical 6*10 = 60;

Angle between hour and minute hand = 155-60 = 96.

Reflex angle 360-96 = 264.

Hemanth Reddy said: (Oct 12, 2015)  
5 hrs 10 min's (given) > 1 hr = 30 degrees > 5 hrs = 150 degrees.

60 min = 30 degrees > 1 min = 0.5 degrees > 10 min = 5 degrees 5 hrs 10 min = 150+5 = 155.

Mohd Faisal said: (Oct 22, 2015)  
Formula = (Section-Difference) multiply by 30 +or- minute/2.

According to Formula time = 5:10.

(10-5) multiply 30+10/2.

= 5*30+5 = 150+5.

155 is answer.

Tapan Timani said: (Dec 10, 2015)  
How to calculate 5.10 to 31/6 please tell me?

Kunwar said: (Dec 16, 2015)  
I'm confused.

1 min is 5.5 degree or 1 min is 6 degree.

Parul Saxena said: (Dec 24, 2015)  
In the previous question separate degree was calculated for minute hand. Then why in this question separate degree are not calculated for minute hand?

Meena said: (Jan 18, 2016)  
Why do we take it as 31/6 hrs?

Ssrgsssdf said: (Apr 17, 2016)  
Why do we take it as 31/6 hours?

Naveen said: (Apr 18, 2016)  
Angle between hands: 1/2(60H - 11M).

H : Hour.
M: Minutes.

Angle for the Minute hand : 6M.
Angle for the hour hand: 1/2(60H+M).
Reflex angle : 360- Angle.

So for this queestion:

Angle = 1/2(60(5) + (10)).
= 1/2 (310).
= 155.

Rahu said: (Jun 13, 2016)  
@Naveed Mohammad.

Thanks for providing those formulas.

Ajay Kumar Aluvala said: (Jun 23, 2016)  
5:10 = 5+(10/60) = 5+1/6 = 31/6 hrs.

1 hr = 30 degrees,

31/6 hrs = 31/6 * 30 = 155 degrees.

Bhushan Gore said: (Jun 26, 2016)  
Convert the hours into mins so, 12 * 60=720 mins = 360d.

5 * 60+10min = 310 mins =?.
720/60hrs = 12 = 360.
310/60hr = 31/6 = ?
360/12*31/6 = 155.

Riya Shah said: (Jul 6, 2016)  
Also, apply the formula;
Q = 30H + 1/2M.

Put the value of Hour and minutes.

30 * 10 + 1/2 *5,
= 155.

Soundarya said: (Jul 9, 2016)  
5 min past 10.

Number of hours = 5.

Degrees rotated in 1 hour or 60= 30deg.
Degrees rotated in 5 hours = 150deg.
Degree rotated in 10 min = (30/6) =5.
Degrees rotated in 10 min past 5 = 155deg.

Sowmya said: (Aug 6, 2016)  
12pm to 5pm = 5hrs.
1hr = 30°.

Therefore, 5 * 30 = 150°.
Tilting time = 10min.
1 min = 1/2°.

Therefore, 10/2 = 5°.

Ans = 150° + 5° = 155°.

Shreya Raut said: (Sep 8, 2016)  
1 hr = 30° and 1 min = (1/2)°,

So , 5 hrs = 150 min and 10 min = 5°,

Thus 150 + 5 = 155°.

Bhadra said: (Sep 22, 2016)  
Thanks for your explanation @Shreya Raut.

Mehak said: (Sep 29, 2016)  
How 31/6?

Still can't understand.

Mohan said: (Oct 21, 2016)  
How 31/6 will come? Please explain me.

Vinoth said: (Dec 28, 2016)  
Best explanation, thanks @Shreya Raut.

Yash said: (Feb 13, 2017)  
It is too much simple.do not complicate it.

Just convert hours into minutes..so, we can say.

12 hours = 360°.

Convert 12 hours into minutes= 720 minutes,
and 5 hours and 10 minutes= 310 minutes,


So simple formula fir that is;
720 minutes = 360°
310 minues = (?).

So,
Cross multiply it and then divide.

(310 * 360)/720.
It become 111,600/720= 155°.

Mayukumarswamy said: (Feb 18, 2017)  
@ALL.

I AM NEW TO THIS COMMUNITY,
NOW I WANT TO SHARE ABOUT CLOCK,
BEFORE GOING TO ATTEMPT ANY CLOCK PROBLEMS,
1.HOUR'S HAND TAKES.
=============HOURS HAND/ SHORT HAND=============
Time to finish one cycle = 360's.
i.e in 12hrs of time =360 degrees.
Within 1 hour of time = 360/12 =30 degrees.
Which means 60 mins = 30 degrees.
In one minute = 1/2 degree (half degree).
=============MINUTES HAND/ LONG HAND=============
Within 1 hour of time =360 degrees.
Which means 60 mins = 360 degrees.
In one minute = 360/60 = 6 degrees.

I think this stuff will help to solve any clock problem.

Tejas said: (Apr 16, 2017)  
Why we multiple it by 31/6?

Bhimnadh Ravi said: (May 29, 2017)  
There are 5 hours between 12 to 5.
We know that 1hr =30 degree,
So 5*30=150degree,
We have 10 min.
So 1min= 1/2 degree,
10min= 10/2 = 5 degree,
By adding 5+150= 155 degree.

Mudasir Rashid said: (Oct 8, 2017)  
Firstly, convert 5hrin minutes.
5*60=300
Add 10 min
=310min.

Now convert 310min in hr.

310min=310/60=31/6hr.
1 hr=(360/12)°.
31/6hr=(360/12)*31/6=155°.

Thambi said: (Nov 8, 2017)  
Hint : Clock started at noon therefore 10min past of 5 means that the clock time is 4:50
hence, now observe the clock 12(-6),1,2,3,4,5,6,7(-1),8(-2),9(-3),10(-4),11(-5) here - indicates opposite.

So now 4:50 means 4 is hours hand 50 is min hand which is -4.

Therefore 4-4=180(complete cycle). Now answer is (180-(50/2))=155. Why 50/2 means 50 is min covered, we know in 1hr it covers 30 degrees then in 1min it covers 1/2degrees therefore in 50min it covers 50/2 degrees.

Veeeateja said: (Feb 4, 2018)  
1 hour it takes 30 degree, 5:10, 5*30=150, 1 miniute =1/2.

10 miniutes =5, total =150=5=150.

Renoop said: (Mar 4, 2018)  
(30*hr+11/2*min)-360.
(30*5+11/2*10)-360=155.

Anil said: (Apr 28, 2018)  
5 hours + 10 minutes.

5*30°+ 10*0.5° {Angle made by hour hand in 1 hour =30°, the angle made by hour hand in 1 min=0.5°}
150°+5°
155°.

Kailash Patria said: (May 2, 2018)  
Hour hand completed 150 (90+60) upto 5 o'clock.

Now, for more 10 minutes past hour hand will move 5° (30° in 60 minutes multiplied by 10 (i.e. 1/2 degree per minute).

Hence total movement 150+5=155.

Suhana said: (Oct 1, 2018)  
Hello everyone.

min=10 past=5 it means,
10 hours 5 min,
so, 10+5/60 = 31/6,
Therefore, hour hand = (360/12 * 31/6) = 155 Ans.

Phaneendra said: (Dec 14, 2018)  
10 min past to 5 means time is 4:50.

Ravikiran said: (Dec 23, 2018)  
1hr=30degrees.

Therefore 5hr and 10min=5*30=150=X.
=10min=5degree=Y,
Z=X+Y,
Z=150+5,
Z=155 degree.

Akhila T S said: (Jan 29, 2019)  
31/6 means the time is 5:10.
5 * 10/60 = 31/6,
1hr-30 minutes then,
31/6 * 30 = 155°

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