Aptitude - Clock - Discussion

Formula:
The angle between minute & hour hand (Ans) = (11/2)minute - 30*hour.
Reflex angle = 360 - ans.

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.

I think 192.5 is the right answer.

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

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.

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.

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.

To find the reflex angle between the hands of a clock at 10:25, we follow these steps:

1. Find the angle of the hour hand:
- The hour hand moves 360° in 12 hours, so it moves 360°/12 = 30° per hour.
- By 10:00, the hour hand is at 10 × 30° = 300° from the 12 o'clock position.
- Since it is 25 minutes past 10, the hour hand moves a bit more. The hour hand moves 30°/60× 25 = 12.5° in 25 minutes.
- So, at 10:25, the hour hand is at 300° + 12.5° = 312.5°.

2. Find the angle of the minute hand:
- The minute hand moves 360° in 60 minutes, so it moves 360°/60 = 6° per minute.
- At 25 minutes past the hour, the minute hand is at 25 × 6° = 150° from the 12 o'clock position.

3. Find the angle between the hands:
- The difference between the positions of the hour hand and the minute hand is |312.5° - 150°| = 162.5°.

4. Find the reflex angle:
- The reflex angle is the larger angle, which is 360° - 162.5° = 197.5°.

So, the correct answer is: d) 197.5°.

To calculate angle : (60h - 11M)/2.

This formula is used to calculate the angle between the hour hand and minute hand.
For 10 : 25;
Using formula : ( 60 x 10 - 11 x 25 )/2,
= 325/2.
Reflex angle = 360 - 325/2 = 197.5.
So, the answer is 197.5.