Aptitude - Clock - Discussion

Please let me know why "Angle traced by hour hand" is calculated for 125 /12 hrs

I got the answer for my previous question. But one more thing I want to now is how reflex angle calculated . and why?

Angle traced out by hour hand in 1 hour = 360/12 = 30 deg.
Angle traced out in 10 hours = 300 deg.
angle traced out in (25/60) hrs. = 30 *5/12= 25/2
total angle = 300 + 12.5 =312.5 deg

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.

The angle between an hour =30°.
Between 10 and 25(5) there are 7 hour.
Therefore 30° * 7 = 210°.
As at 10:25 the hour needle is 25 more than a perfect hour,
Therefore we have to minus 25/2 by 210° (as the angle between a minute is 1/2,
=> 210°- 25/2,
=> 210° -17.5 =192.5.

Use direct formula.

Which is used to find angle between the two hands at a time, h, m is;
30*h - 5.5*m.
So here,
h=10, m=25.
300*10 - 5.5 * 25 = 162.5.
360 - 162.5 = 197.5 (option D).

Angle=(60*h-11*m)/2.
And reflex angle=360-angle.

For some angle θ (theta),
Original angle = θ ,
Reflex angle = (360 - θ).

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.

Angle needed:

1} Hour hand to go from 10.25 to 12 i.e. (35+60) = 95min = 47.5° (speed of hour hand is 0.5° per minute)

2} Minute hand to go from 0 to 25 = 150°(speed of minute hand is 6° per minute).

Ans: 47.5 + 150 = 197.5°.