Aptitude - Clock - Discussion

Please tell me how we are getting 21/4.

Angle between them 1 hour is 30 degree so 30+30+30/4=67.5.

Basic calculations first :

In 1 min Angle traced by Hr hand=1/2 degree.
And in 5 min angle traced by minute hand = 30 degree.

So now,

In 15 minutes hour hand movement = 15*1/2 degree=7.5degree
and distance between minute and hour hand at 5.15 O'clock is calculated as,

10 minutes + 7.5 degree(hour hand extra movement in 15 minutes).

So,

As per our calculations,

5 minutes => 30 degree (for minute hand).
10 minutes => 60 degree.

So,

(60+7.5) degree = 67.5 degree.

Theta = 1/2(60*h-11*m) (formula).

Where h = hour and m = minute.

5.15 = 1/2(60*5-11*15).

= 1/2(300-165).

= 67.5.

What is past 5? which means what?

Using formula to calculate angle i.e. 1/2(60*h-11*m) where h is hour time and m is minute, angle can easily be calculated.

Total no of points between any two no in watch for hour is 6. And for minute is 5.

Then angle between any two points for hour is 5 degree. And such for minute is 6 degree.

So when hour needle move one point between any two no then minute needle move 6 degree so the angle between any two no like 4 to five be 30 degree.

So cover 5 degree (for hour) = 10 degree (for min).
So 1 degree = 2 degree.

So when min needle travel 1 degree then hour needle cover 1/2 degree.
So for 15 minute it will cover 15/2 = 7.5.

And degree from 3 to 5 be 60 degree.
So total = 60+7.5 = 67.5.

5+15/60 = 21/4 is correct.

@Sagar.

If 5+15/60, then why again 15 minutes is considered separately and solved in the answer?

21/4 = 5 hr 15 min = 5(15/60) = 5(1/4) = ((5*4)+1)/4 = 21/4.