Aptitude - Clock - Discussion

As simple as that in 60 min(1hr) hour hand (small hand) turns 30°.
Means every hour small hand turns 30°
So if we calculate then imagine the hour hand and min. Hand position
By that you get min hand will be on 5 and hour hand on 10 (not exact but slightly upwards)
So 1st calculate the angle from 5-10 it would be 30+30+30+30+30 = 150

From 5-10 it's 150°
Now the hour hand has moved slightly upwards but how much?
So to find its easy from the above statement i said
If 60 min =30°
Then 25 min= ?

Cross multiply it ;
It gives 12.5.
So now add 150+12.5 = 162.5.

So the question was to find reflex angle which means the angle should be between 180° - 360°.

So to calculate that just do substraction of angle we found between 5-10 from whole circle

360-162.5= 197.5°.

Step1. find angle b/w 12 and minute hand. ( ie, 150 °)
Step2. find angle b/w hour hand and 12,
Step3. Add angles.

* In 1 hr the hour hand moves 30 degree --> ( 60 * 30 )/60,
*from 10 to 12 --> 60 degree.

In 25 minutes hour hand moves 25 * 30 / 60 degree --> 12.5 degree.
Angle b/w hour hand and 12 is--> 60 - 12.5 = 47.5 degree.
47.5 + 150 = 197.5 degree.

The 2 most confusing terms here are :
1) How did you get 125/12 and,
2) How did you calculate the reflex angle.

Solution:
Answer for 125/12:

-> 10.25 will be the same as 10 hrs and 25 minutes. now you need to convert 10 hrs and 25 minutes into a single value of hrs.

i.e 10 + 25/60 ....( since, 60 mins = 1hr and 25 mins = ? hr )
which is equal to 25/60 hr.
->now 25/60 can be written as 5/12.
->10 + 5/12 which is equal to 10.4166 or 125/12 in terms of fraction.

Answer for reflex angle :
-> Angle between 180° and 360° is reflex angle.
->simply, subtract your angle from 180° if it is greater than 360°.And subtract your angle from 360° if it is less than 180°.

@All.
I will explain it.

Hour Hand Makes 30 Degree In 1 Hour(1 Hour------->30 Degree)
Minute Hand Makes 6 Degree In 1 Minute(1 Minute--------> 6 Degree)
So For Hour Hand;
10:25 ---------------> 10 Hour + 25/60(Because Hour Hand Covered 10+(plus) something that is 25 Minutes More Which Cause We Takes 25/60 Hour More).

= 10+25/60.
= 10+5/12.

Total Hours Covered By Hand Hour=(120+5)/12=125/12;

Now;
Convert It Into Degree=(125*30)/12=625/2 Degree;
...................................................................................
Now For Minute Hand.
25 Minute;
Convert It Into Degree= 25*6=150;
.................................................................................
Find Angle B/w Hour Hand & Minute Hand
so;
= 625/2-150
= (625-300)/2
= (325)/2 Degree;
A/c Question We Need To Find Reflex Angle (an angle greater than 180° and less than 360°)
so;
Total Clock Degree=360 Degree.
so,
=360-325/2.
=(720-325)/2.
=395/2.
=197.5.

(11M-60H)/2.
= (11*25-60 * 10)/2,
= (325/2) = 162.5.

The reflex Angle is 360-162.5 = 197.5 degree.

Hour hand is not exactly at 10:00. It has passed 10:00.

@Meghna

Because in 25 minutes the hour hand would have moved ahead of 10. (At the rate of 0.5' per minute) '.

It was exactly at 10 when the minute hand was at 12.

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°.

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.

@All.

10.25 is actually ten hours and 15 mins (.25*60).