Aptitude - Clock - Discussion

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°.

@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.

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.

I don't know people are so confused over these small problem let me make you all clear. Hear we know 60 min = 360 degree.

& 12 hrs =360 degree.

When time is 10.25 it means hour hand is slight ahead 10 not exactly at 10 so 10.25 = 125/12 as said earlier so calculating angle using hour relation by unitary method its getting 312.5.

Now calculate the angle made by minute hand i.e 25 minutes it makes (360=60) *25=150 draw a clock and see the angle made by hour that is 312. 5 degree from 12 o clock and similarly see the angle made by minute hand its 150 degree from 12 0 clock here if reflex angle is asked so which is angle made by them in anticlockwise direction. Since clock rotates in clock wise direction. If you are not getting reflex angle just remember as anticlockwise concept. Hope you get it my friend.

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°.

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°.

10:25 = 10 hrs + 25 min. Therefore, total angle between them.

[angle at 10 hrs (=60 deg) + angle during 25 min movement (=150(min needle)-12.5(hrs needle) = 137.5 deg)]

= 60 + 137.5 = 197.5 or 197(1/2) degree.

Refer explanation below:

At 10 hrs, angle between them = 60 degree.

During 25 min movement both needle will move. At 25 min minute needle will make an angle = 25 x 30 = 150 degree.

Simultaneously, hrs needle also will move an angle = 12.5 degree. (as hrs needle make 360 degree in 12 hrs or 720 min. Therefore, in 25 min, angle = 25x360/720 = 12.5 degree.).

There is no easy way to understand in spite of this explanation.

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°.

Kindly find my observation for the above question is.

I. Minute hand takes 5 minute that is 300 seconds to complete a 30* space
therefore in 1 sec; 1/10 degree space it covers.

II. Hour hand takes 60 minute that is 3600 seconds to complete a 30 degree space
therefore in 1 sec; it covers 1/120 degree space.

Therefore in 25 minutes,
minute hand rotates to 25x60x1/10 = 150 degree.
and hour hand moves to 25x60x1/120 = 17.5 degree.

ie., in 25 minutes from 10 o'clock; minute and hour hand forms an angle of 192.5 (150 + 30 +(30 - 17.5)) degree.

Therefore the reflex angle will be 167.5 degrees.

Please correct me if I am wrong.

They asked reflex angle.ie (360-Shortest angle) = which is basically the biggest angle made by both hands Which is nothing but the clockwise angle.

Now, if it's time 10:25, so the minute hand is at 5 on the clock and the hour hand is above 10 and below 11 to be precise. Slightly below the Middle of 10 and 11.

So, the angle in a clockwise direction will be, from 11 to 5.

It's 180° and from hour hand to 11, it's 15+2.5 ( 15 for the middle of 10 to 11, and 2.5 for slightly below part, analyze in your home clock, everything will be clear).

So, the total angle is 180+15+2.5=192.5°.