# 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°

 Aisha Raja said: (Jul 21, 2019) @Thongoc992. It says at the START of noon which is 12 o'clock.

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