Aptitude - Clock - Discussion

To find the angle use this formula:

Θ=|5.5*(min) - 30*(hour)|
here in this example;
θ = |5.5*25 - 30*10|
= |137.5 - 300|
= |-162.5|
= 162.5 for an obtuse angle.

Now for reflex angle 360-162.5 = 197.5.
Using this formula u can find min and hours using theta or angle.

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.

30H -11/2 * M
30*100-11/2 * 25 = 162.5
360-162.5 = 197.5.

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°.

Angle between hrs and min formula is 30H-11/2 M, we get 263 1/2.

Now reflex formula is 360-263 1/2 = 197 1/2.

1hr---> 30°
Then 8hr --->240°
As we know 60min --->30° than for 25 min ---> 12.5.

Now, 8hr25min forms --->240+12.5=252.4,

as the minute hand is at 5 then the angle of the minute hand becomes 5*30=150,

Now the angle b/w the hands will become 262.5-150=102.5,

But the question is about the reflex angle.so,360-102.5= 197.5.

Reflex Angle Means an angle greater than 180 degrees but less than 360 degrees.
At 10 hr Angle = 30×10 = 300 degree.
For 25 min Angle= (25×5.5) = 162.5 degree (because 5.5 degree/min is the relative speed between min and hours hand)
Normal angle= (300-137.5) = 162.5 degree.
Therefore, Reflex Angle= 360-162.5= 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°.

I think 192.5 is the right answer.

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

The reflex Angle is 360-162.5 = 197.5 degree.