20-the angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

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The logic follows here is :-

Hour hand covers 3600 in 12 hours
Angular distance covered in 1 hour = 360/12 = 300
Angular distance covered in 60 minutes = 300
Angular distance covered in 1 minutes = 1/20

Calculation :

Minute hand covers 3600 in 60 minutes
60 minutes = 3600 1 minute =360/60

1 minute = 60

Angle covered by minute hand = 20 × 60 = 1200

Angle covered by hour hand = 6 × 30 + 20 × 1/2 = 1900

Angle between hour and minute hands = 1900 - 1200 = 700

Hence, the angle made is 700.

By applying the formula we can get the answer is:
Angle = |[11/2M ± 30H]|
Where M = 20 and H = 6

Thus, the correct answer is "700".

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Discussion :: Clock - General Questions (Q.No.8)

Clock - Important Formulas
«« Clock - General Questions

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

[A].	0°
[B].	10°
[C].	5°
[D].	20°

Answer: Option B

Explanation:

Angle traced by hour hand in	13	hrs =		360	x	13		°	= 130°.
3	12	3

Angle traced by min. hand in 20 min. =		360	x 20		°	= 120°.
60

Required angle = (130 - 120)° = 10°.

Kittu said: (Aug 23, 2010)
Please give clear formula how 13/3 came?

Sundar said: (Aug 31, 2010)
Hi All, We can write 4 hrs. 20 mins. as 13/3 hrs. 13/3 = 4 and (1/3)hrs = 4.20 ( Here 1 hour = 60 mins, 1/3 of 60 is equal to 20). Hope you understand guys. Have a nice day!

Reddilavan said: (Oct 31, 2010)
angle=(11/2)min-30hrs apply this formula you can get the answer ......

ANUJ said: (Dec 22, 2010)
we can convert it in hours as: 20min.=1/3hours so total hours as 4+1/3=13/3

Nitin said: (Dec 28, 2010)
By common sense it is clear that in 20 minutes the minute hand will move 206=120degree and the hour hand will move20(1/2)=10degree. Clearly min hand will be at 20 and hour hand will be 10degree apart.

Prasad said: (Jan 5, 2011)
Apply the formula suggested by Reddilavan.. ie: Angle = 30Hr-(11/2)Min

Srilu said: (Apr 27, 2011)
In first can we take 12/3 instead of 13/3 ?

Arc said: (May 28, 2011)
Thanks Sundar.

Karan Bajaj said: (Jun 1, 2011)
Hi girls ! we can write 4.20 also as 13/3, we covert 20 min into hrs 20/60=1/3 and we add with4 hrs 4+1/3=13/3. Have a nice day.

Anil said: (Oct 29, 2011)
Direct formula: \|11M-60H\|/2 where M=minute, H=hour hands.

Saum said: (Nov 18, 2011)
Why we are substracting angle traced by hour hand and angle traced by minute hand ? One another thing is that - if we see the clock at 4.20 hour hand is at 4 and minute hand is also at 4. So angle between them must be 0 degree. Please clear me.

Aashish said: (Jan 3, 2012)
I agree with Saum. Can someone please clear our doubt?

Tejkishor said: (Jan 29, 2012)
@Saum We take 12 O'clock point as reference point (r.p). So we subtract the angle move by hr hand from the r.p. and the angle move by the min hand from the same to get the separating angle between them and also at 4:20 the hands doesn't coincide in my watch.

Javan said: (Jan 31, 2012)
Thanks anil..

Hemant said: (Feb 1, 2012)
We can also mark the ans by common sense..ie, 1. It is clear that the angle could not be 0. 2. Since the hour hand leads the min hand, and it will be in between 4 to 5, if the time will be 4.30, hour hand exactly in mid of 4 n 5, i.e 5min=30 degree, than half is 15 degree if the time would 4.30, but it is less than the 4.30, so angle will be slightly less than the 15 degree.

Mouparna said: (Feb 27, 2012)
Thanks Prasad.........

Raviteja said: (Mar 17, 2012)
Here is a simple formula to get an angel between hands.. 30[ Difference b/t hours and ( min /5) ]+ (min/2) Take an example 4:20 30[4~20/5]+(20/2)=0+10 = 10

Prasant said: (Mar 29, 2012)
60 parts by min hand = 5 parts by hr hand. 20 parts by min hand = (5/60) *20 = 1 2/3 part by hr hand. 1 part = 6 degree. 1 2/3 part = 10 degree.

Mohan said: (Jul 14, 2012)
To find angle take this formula. Angle= ( (11/2) min-30hour). If we get angle value as negative take that value as positive. That will be the answer.

Nikhila said: (Nov 28, 2012)
Hey all. We know that the minute hand is at 4 at 4. 20. We jst hav to calculate the angle moved by hour hand from 4 for 20 min. For 60 min, Hour hand covers 360/12=30 degree. For 20min, it covers 30*20/60= 10 degree. (Just cross multiply. ).

Arko said: (Jan 12, 2013)
The formula is 30h- (11/2) m.

Amit Goswami said: (May 19, 2013)
12h - 360 degree. 1260 min --> 360 degree. 1 min -- > 360/1260. 20 min --> 20360/(1260). -->10 degree.

Karthiga said: (Oct 28, 2013)
To Anil. Will the formula be applicable to all the problems sir?

Praneeth said: (Nov 10, 2013)
Divide into 12 parts each division 30 deg. for hrs. hand for every min it moves by 1/2deg. 20 min = 20*1/2 = 10dg that's it.

Navya said: (Dec 26, 2013)

In the above someone said apply direct formula that is: 11M - 60H/2. Can this formula be applicable to all problems guys.

Explain please.

Ali Zohair Shah said: (Mar 24, 2014)
It is 4 degree. Because hour hand moves 30 degree in 1hour. So it is 1/3 hours passed so it rotates 10 degree. Total angle of hours hand is 304+10 = 130 degree. Minute hand moves 6 degree in 1 minute = 206 = 120 degree. So 130-120 = 10 degree.

Chaturbhuj Singh said: (Apr 28, 2014)
4:20 = 4 +20/60 = 4+1/3 = 13/3.

Anurag Nayak said: (Aug 13, 2014)
Start at 4 pm. minute hand has to travel 20 min. We know, 5 min gain by hour hand in 1 hour/60 min. ?? min gain by hour hand in these 20 min. 5/60 * 20 = 5/3 min. We know 5 min is 30 degree. 5/3 min is 30/3 = 10 degree. Simple.

Jawahar.s said: (Aug 17, 2014)
360/12 4 = 120. 360/60 20 = 120. 120-120 = 0.

Gaurav Verma said: (Aug 24, 2014)
We can write 4:20 in fractional form 4(20/60). Means, (60 *4 + 20)/60. Equals, 13/3.

Dolagobinda Behera said: (Aug 31, 2014)
As @Anurag answers it is the degree achieved in 5/3 minute by hour hand but how is it related to the angle being asked between the hour hand and minute hand in the question ?

Lakshmi said: (Nov 1, 2014)
As we know 12 hrs = 360 deg. i.e, deg's between hr to hr is 30 deg. 1 hr = 60 min. We want degree for only 20 min. 20 min = 10 deg. 40 min = 20 deg.

Monika said: (Feb 21, 2015)
What is 360/12 & 360/90? Just make it clear please.

Javed said: (Feb 28, 2015)

So simple guys. Total 360 degrees. Total clock = 12 hours. 360/12 = 30 degrees. That is 1 hour = 30 degrees. 1 minute = 360/60 = 6 degrees. 1 min = 6 degree. 1*20 = 6*20. 20 min = 120 degrees -----> 1st equation. Simplify: = 4 (1/3) (i.e 4 hr and 20 min). => 4*3+1/3. =12+1/3. = 13/3. = (13/3)*(360/12). = (13/3)*30 {cancel 3*10 = 30}. 13*10 = 130 ------> 2nd equation. Remove 1st equation and 2nd equation. 130-120 = 10 degrees.

Answer is 10 degrees.

Rouf said: (Mar 16, 2015)
At what time between 1pm and 2pm the angle between hour hand and minute hand is 168 degrees?

Saisumanthkosuru said: (Apr 25, 2015)
What is angle between 4 hours 10 minutes?

Sanapala Durga Prasad said: (May 16, 2015)
30H + 0.5M - 6M = 304 + 0.510 - 6*10 = 65 deg.

Harish said: (May 22, 2015)
Hello @Javed, You have explained the solution clearly, but in the simplifying process. = 4(1/3) (i.e 4 hr and 20 min). => 4*3+1/3. Here in this above step 4(1/3) should become 4/3 right.

Tamizh said: (Jun 8, 2015)
Thanks Mr.Prasad for clearing my biggest doubt in this chapter by using that formula. i.e 30hrs-(11/2)mins. That was helpful.

Junaid said: (Jun 12, 2015)
Its so simple guys. Total 360 degrees. Total clock = 12 hours. 360/12 = 30 degrees. Now 1 hour = 30 degrees. 1 hour = 60 minutes. So 30/60 = 0.5 Degrees. Now 1 minute = 0.5 Degrees. Just multiply DegreeMinutes. = 0.520 = 10 Degree.

Greeshma said: (Jun 12, 2015)
I think the formula you given (11M-60H)/2 is wrong, It is not coming can you explain it? For example the angle between the two hands at 6:00 it is giving wrong answer.

M Rajeswari said: (Jul 9, 2015)
It is correct 11/2(20)-30(4) = 110-120 = 10.

Shashank said: (Aug 17, 2015)
@Greeshma. Angle between 2 hands at 6:00. MIN (M) = 0. HOUR (H) = 6. Formula is (\|11M-60H\|) /2. So, {\|11(0)-60(6)\|}/2 = 180. That's it :-).

Sandhu said: (Aug 29, 2015)
Please tell me how makes formula 11m -60H/2?

SANKET RANJANE said: (Oct 8, 2015)
Its simple. Just remember for hour hand it covers 0.5 degree in one minute. And minute hand covers 6 degrees.

Rahul said: (Nov 3, 2015)
What do we do if we have a reverse question? At what time between 3 and 4 clock will there be 36 degree?

Premsai said: (Nov 7, 2015)
I am not able to understand.

Premsai said: (Nov 7, 2015)
Any another method?

Netsi said: (Feb 16, 2016)
@4:20 is the hour hand @4? It moves a little towards 5.

Satya Prakash Singh said: (Feb 17, 2016)
This formula does not provide solution for all problems. Ex. 11:43. = 6011 - 1143/2. = 187/2 = 93.5. Which is not appropriate angle.

Rajkumar said: (Mar 30, 2016)
What angle will form at 10 clock. Please explain?

Mukesh Kumar said: (Apr 13, 2016)
@Rajkumar. It should be 60 degree.

Aniil Maurrya said: (Jul 10, 2016)
The perfect formula is 1/2\|(60H - 11M)\|.

Gaurav Kashyap said: (Aug 28, 2016)
Apply simple formula \|11/2 * min - 30 * hr\|.

B Mallesh said: (Aug 30, 2016)
In explanation, why 360/12 and 360/60 are taken?

Punithavathi said: (Nov 4, 2016)
The shortcut formula to find angle b/w two hands. 1/2[60H - 11M] where H is hour, M min. If result is above 180 then subtract the answer from 360.

Vivek Akhande said: (Dec 30, 2016)
Direct formula: \|[{(11* Minute) ÷2}-30 * Hour]\| Best accurate formula for finding angle between minutes and hours, coincidence angle, straight line, perpendicular angle and random angle.

Mihir said: (Feb 16, 2017)
Good job @Karan Bajaj.

Rohit said: (Mar 18, 2017)
11/2m-30hr formula is correct for every angle. And another thing ANGLE IN CLOCKWISE DIRECTION IS NEGATIVE.

RAHUL R. PARSODKAR said: (Apr 18, 2017)
SIMPLE FORMULA. 30H - (11/2)M Where, 'H' FOR 'HOUR'; 'M' FOR 'MINUTE'. Answer will generated in degree angle. Note:- Suppose, answer of angle is greater than 180 degrees then answer will be reduced or minus (- 360) from original angle for example 1) 3:40 hr. According to formula, 303 - (11/2)40. = 90-220 = -130 = 130 degree (and take it +Ve).

Aadityan said: (Apr 22, 2017)
Thanks @Reddilavan.

Mukram Khan said: (Apr 27, 2017)
When the time in watch 01:30 what is the angle of needles? Can anyone solve this?

Rahul Gupta said: (Jul 24, 2017)
For 4:20. Basic formula and h and m indicate hours and mint. (H-m÷5)*30-(m÷2).

Shakir said: (Mar 6, 2018)
12 hr = 360°. 1 hr = 30°. 1 min = 1/2°. 20 min = 1*20/2 = 10°.

Ravi Singh said: (May 5, 2018)
Formula :- M=2/11(t130+-°) °=Angle. Solution- 20=2/11(430+-°) 10*11=\|120+-°\|, 110-120=°, 10°= ans.

SIVAKRISHNA said: (Jul 10, 2018)
@Anil \|11M-60H\|/2 formula. This formula is not sufficient for some problems. For example; can you find an angle between the minute hand and hour hand of a clock when the time is 3:40? Solution: \|1140-603\|/2. =440-180/2. =360/2. =180°.

Md Shahrukh Alam said: (Jan 19, 2019)
\|60 * 4-11 * 20\|/2. 240-220/2, 20/2.

Anuranan said: (Feb 3, 2019)
It very simple. 1 Hour cover =30 ° So, 60 minutes cover 30 °. 1 minutes cover 30/60 -_1/2 °. 20 minutes cover 20 (1/2) °. Equal to 10 °.

Ansh Shukla said: (Jan 5, 2020)
How 1-hour cover 30°? Can anyone clear this? please!

Aditi Pawar said: (Jul 31, 2020)
12 hour covers 360 degrees. Then 360/12 = 30 degrees. That is one hour.

Omkar said: (Sep 17, 2020)
Just use this formula. A = 30 * H - 5.5 * M. Where; A = angle. H = hour. M = minutes.

Durga Prasad Ullingi said: (Oct 16, 2020)
4hours :20minuts angle = 20/2. = 10°.

Hashir Usmani said: (Apr 18, 2021)
Can we do like this; (20/60)*30 = 10?

Omkar said: (Jul 7, 2021)
Short trick for these ans. Take a ratio of 4.20=1:5 then there is a formula, when ur ratio is 1:5 then, divide minutes by 2 i.e 20÷2 = 10. Also when ratio is 1:8 then (minute-hours) * 2 Also for the ratio 1:3, = minute * 4+minute ÷2 Ratio 1:10, θ = minute2.5. 1:4then θ= minute2. 1:6 θ = minute ÷2.

Anil said: (Oct 26, 2021)
For 1 min the Hr hand moves 0.5, So, the angle between Hr and Min hand is =0, Since Min Hand moves 20 mins. We have 20*0.5=10. Therefore 0 + 10 = 10.