Aptitude - Clock - Discussion

From where did you get 125/12?

Hi, friends.

It is very simple when we are calculating for hours hand we divide it by 60mins
while for minutes, we divide it by 60.

@Akshay

Please give me the derivation of this formula Angle=|30(hh)-11/2(mm)|.

This is very simple method.

10.25 means hour hand is at 10 and the minute hand is at 5. So angle between them is 10 - 5 = 5hrs.
Since 12hrs is 360 degree.

1hr = 30degree. So, 5 * 30 = 150degree. But when it is 25minutes.

We have a small angle that has to be added ie. 25minutes = 12. 5degree.
Since 1minute is 1/2degree.

Therefore 150 + 12.5 = 162.5.
But they asked reflex angle so, 360degree - 162.5degree = 197.5degree.

Friends its very simple.

Every minute 6 degree will be the movement of the minute needle, ok.

So, the movement 360 degree of the second needle is 6-degree movement of the minute needle. Ok

Again every 6-degree movement of the minute needle will give rise to 0.5 degrees of hours needle, ok

Calculate the distance between 25 minutes to 50 minutes , u will get 6 * 5 * 5 =150 degree
Now calculate the movement of only hours needle i.e between 50 to 55 for that you have to calculate the movement of minute needle i.e 25 minutes.

Now one minute's movement of minute needle rises the distance of 0.5 degrees the for 25 minutes = 25 * 0.5 = 12 1/2.

We have already 150-degree distance between 25 to 50 now we will add 150 + 12 1/2 = 162 1/2.

The whole clock has the distance of 360 degrees then the reflex angle is
360 - 162 1/2 = 197 1/2. It's one of the ultimate explanation.

Simple calculation:

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

Now add it with 360.
360 + (-162.5).
197.5 -> 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°.

60 minute = 360°.

1 minute = 6°.

In the case of hours clock;

When hours clock moves one hour (30°) then at the same time minutes hand cover 360°.

360°/60= 6 that's us one minute.
30°/60= 1/2.
Means in every one minute hours hand covers (1/2)°.

Now solve the problem;

25 * 6 = 150° (for minute hand).

50 * 6 + 25 * (1/2) = 312(1/2) ° (for hour hand).

We calculate here bigger angle so,

360° - (312.5 - 150) = 197.5°.

Another shortcut way we can use for this problem.

150° for minute hand.

10 * 6 = 60°.
25 / (1/2) = 12.5°.
150° + 60° - 12.5° = 197.5°.

Angle moved by hours hand in 25 min. Is (25/2) degree. So angle between hour hand and 12 position is 60-25/2 degree. And angle between 12 and min hand is 150 degree. So reflex angle 60-25/2 + 150 degree.

At 10.25, if the hour hand would stay at 10, the angle between hour and min hands would be 180°. But because it moves, the angle by which the hour hand would've deviated from 10 in 25 mins would be;

60 : 30 :: 25 : x (In one hour the hour hand moves by 30°)
x = 12.5°
So, 180 + 12.5 = 192.5°.

Can somebody please tell me where I am going wrong?