Aptitude - Clock - Discussion

How 22 times in 12 hr?

It should be 48 times.

Because for 1 hour right angle will be 2 times.

The answer is 44.

The minute hand moves 360 degrees in 60 minutes. This means that the angle of the minute hand is given by 6t, where t is number of minutes past midnight.

The hour hand moves 30 degrees in 60 minutes. This means that the angle of the minutes hand is given by 0.5t.

The hands start together at midnight. The first time they make a 90 degree angle is when the minute hand has moved 90 degrees further than the hour hand, so this is given by the equation:

6t = 0.5t + 90
5.5t = 90
t = 16 4/11

In other words about 16 minutes past midnight.

The next time is when the minutes hand has gained another 180 degrees on the hour hand, and is 90 degrees behind it:

6t = 0.5t + 270
5.5t = 270
t = 49 1/11

At about 11 minutes to 1 o'clock.

For every 180 degrees that the minute hand gains on the hour hand there will be one 90 degree angle, so every
49 1/11 - 16 4/11 = 32 8/11 minutes

24 hours is 1440 minutes.
1440 / (32 8/11) = 44.

So every 24 hours there are 44 right angles between minute hand and second hand.

At what time between 4 and 5'o clock will the 2 hands of a clock be
at an angle of 60 degrees with each other?

How 22 times in 12 hr?

@chandra....ur answer is 32 8/11 mins past 4....corect me if i m wrng

Hi guys... Its simply only, for every 1 hr the min hand and the hour hand are right angles at 2 times so someone blindly calculate
24*2=48 actually its wrong ... at the time of 8 and 2 o clock the hands are right angles at 1 time 1y i.e right angle means both the hands have 15 min space, at the time of 8 & 2 both hands are right angles at 1 time only so 10*2=20 20+2=22

So in 12 hours, they are at right angles 22 times.
In 24 hours, they are at right angles 44 times.
try it with 1 time piece ... u will understand clearly.

In 60 min. 55 mins are gained by minute hand i.e. in 1 hour, hour hand lags by 5 mins.
in 12 hrs. , hour hand lags by 12*5=60 mins. i.e. 1 hr.
and in 1 hr dere r 2 right angles
hence in 12 hrs. 2 right angles will be lost resulting 22 instead of 22 and hence 44 in 24 hrs.

@prashant:

When 55 minutes are gained by minute hand then after 1 hour hand should lag by 55 minutes and not 5 minutes

@shiva karthik correct me if i am wrong. At 8oclock also the hands will be at right angle at 8 25 and 8 55. Thus it happens two times at 8 o clock also. so how it will be 22 times.