Aptitude - Clock - Discussion

This is the best way 10:25.

First find the minutes 10 hrs x 60 min.

600 mins + 25 mins = 625 mins and then divide by 60 because I cycle is 60 mins. So 625/60 reduce so 125/12 multiply by 360 degrees over 12 hrs.

360/12(125/12) (360/12) = 45000/144 = 312.5 degrees/hr. So that's, your degrees in hour and then find degrees in 25 minutes. 25 mins x (360/60) because 360 degrees 60 mins.

9000/60 = 150 degrees. Then degrees in hour - degrees in minute. 312.5-150 = 162.5 degrees. Then 360 degrees - 162.5 degrees = 197.5. Because reflex angle are not less than 180 but not more than 360.

Reflex angle = 360-(angle between hours hand and minute hand).

/*10.25 it can be written as in hrs.*/

Total hours = (10+25/60) = (10+5/12) = (125/12).

Angle traced by hours hand = (125/12)*(360/12) = 312(1/2).

Angle traced by minutes hand = 25*(360/60) = 150.

Angle between 2 hands = 312(1/2)-150 = 162(1/2).

/*The angle formed by a both hands and a perpendicular to the surface at the point of reflection.

Here the surface is circular so ref angle is 360.
*/

Reflection angle = 360-(Angle between 2 hands).

= 360-162(1/2).

= 197(1/2).

Reflex angle means angle more than 180 but less than 360 . So, we should calculate larger angle not smaller angle betwn the hands . We can choose the angle between the hands in two ways one more than 180 and other less than 180(obtuse) .

10.25 hr =10hr + 25min = 10hr + 25/60hr = 125/12 hr

So, the angle movie by hr hand from 0 hr point(12 in our watch) is

360/12 * 125/12 = 312.5

Angle move my minute hand from 0 hr point is 360/60 * 25 = 150

So the smaller angle(obtuse) between the hands is 312.5 - 150 = 162.5

So the larger i.e. reflex angle = 360-162.5 = 197.5

If you use the formulae the answer would be simple.
Instead of confusing in theoretical way.
Formulae
If hrs>6,
30hrs-(11/2)*min=angle,
else if hrs<6,
11/2*min-30hrs=angle,

In this sum
hrs=10;min=25,
since hrs>6 use 1st formulae,
subtitute ; 30*10 - (11/2)*25=angle,
angle=162.5,
sincle they have asked reflex angle,
reflex angle =360-162.5=197.5(only for reflex angles).

Formulae 1 & 2 are mostly used in clock problems
if they ask what is the minute and gave right angle or opposite angle, substitue the angle as 90deg or 180deg and proceed the sum.

I think, it's 197.5 deg.

For 1 deg min hand ---hour hand rotates by 1/12 deg.
So for 10 hours, the hr hand rotates by 10*30=300 deg.
Again for 25 min --- min hand rotates by ---- 25*6 = 150 deg.
So for 150 deg rotation of min hand hour hand rotates by 150/12 = 12.5 deg.
So total hour hand rotation is 300+12.5 = 312.5 deg.
Now the angle left to rotate to complete 1 full rotation is 360-312.5 = 47,5 deg.
The reflex angle will be 150+47.5 = 197.5 deg.

It is asked to find a reflex angle not obtuse angle so the given answer is 100% right.
Thank You.

Given, time= 10:25.
Here, h= 10, m=25.
h= hours. &. m= minutes.

Formula is Angle=[ 30h-(11m/2)].
=[30*10-(11(25)/2].
=[300-(275/2)].
=[(600-275)/2].
Angle =[325/2].

Reflex angle= total angle- actual angle.
= 360-(325/2),
= [720-325]/2,
= 395/2,
= 197*1/2.

In this, we have to use the formula ∠=[30h-(11m/2)].

Hand at 10:25,it means;

See Hour hand first, in terms of minutes=10*60+25 = 625min.
Convert it into Hours,:625/60=125/12 (Divide in both by 5).
Since we know angle made by Hours hand is: in 12Hours = 360degree.
So in 1Hours=360/12=30degree.

So in 125/12Hours=125/12 * 360/12=45000/144 = 312.5 = 312 ,1/2degree.
In Minutes hand in 25Min = 25 * 6 = 150degree.
Angle between Hands = 312.5 - 150 = 162.5degree.
So, the Reflex angle = 360 - Angle between Hands.
360-162.5=197.5.
it means 197 1/2 is the correct Answer.

My suggestion in solving clock problems, we better to calculate in minutes. If it is in hours convert to minutes it will be easy. Hope you people understand.

Movement of minutes hand in each minute = 360/60 = 6°.

Movement of Hour hand in each minute 30/60 = 1/2°.

10 hour 25 minutes = 625 minutes.

Therefore;.

625/2 = 312.5°.

25 * 6 = 150°.

Angle between the hands of the clock when the time is 10.25.

= 312.5° - 150°. = 162.5°.

Reflex angle = 360 - 162. 5 = 197.5°.

In hour hand, the angle between 12 pm - 10 pm = 300' + 25 (min) * 0.5 => 625/2 =>312.5.
In minute hand, the angle between 12 pm - 5 pm = 25 (min) * 6' => 150.
The angle between the hour hand and the minute hand is : 312.5 - 150 => 162.5.
So the question was to find the reflex angle which means;
The angle should be between 180° - 360°.
So, to calculate that just do a subtraction of the angle we found between 5-10 from the whole circle;
360-162.5= 197.5°.

For every 5 minutes, the minute hand make a 30-degree angle.

So, from 11 to 5 the angle made by the minute hand is 30*6=180 degrees.
Now we have to find the angle made by hour hand (hour hand in between 10 and 11)
For every 5-minute hour hand moves by 30/12 degrees.

So, for 25 minutes (time is 10.25) the hour hand moves (30/12)*5 =12.5 degrees.
So the remaining angle hour hand make with 11 =30 - 12.5 = 17.5.

Total angle when time is 10.25 = 180+17.5 = 197.5.