Aptitude - Clock - Discussion

Hour hand moves = 0.5 degrees/min.
Minute hand moves = 6 degrees/min.
The angle between the hour hand and the minute hand should be = 90 degrees.
Let the minutes at which hour and minute hand makes 90 degrees = x.

Therefore,
Minute hand angle - hour hand angle = 90 degrees.
6 degree/min * x - (5*60 mins + x) * 0.5 degree/min = 90 degrees.
6 degree/min * x - 150 degrees - x * 0.5 degree/min = 90 degrees.
(6 degree/min * x - x * 0.5 degree/min) = 90 degrees + 150 degrees.
(6 degree/min * x - x * 0.5 degree/min) = 90 degrees + 150 degrees.
5.5 degree/min * x = 240 degrees.
x = 240 mins / 5.5
x = 43.6363 mins.

Hence, at time 5 hour and 43.6363 mins hour hand and minute hand makes 90 degrees angle.

@All.

My doubt is here the question is between 5:30 & 6.

So, for 90degress it's should be 5:45 right? Why did they assume from 5'o clock?

At what time between 5 and 60' clock the hands of a clock will make an angle of 40%?

Anyone, explain the answer.

@Abi and @ Babu.

When two hands coincide after exactly one hour, minutes hand travels one full circle that is 60 spaces but hours hand moves 5 space forward. So after exactly one hour later, they gain 55 spaces are their relative gain.

Please, someone, share the solution of how come40*60÷55 = 7÷11 came ? Pls someone explain it..

55min spaces are gained in 60min. What it is, Can someone explain to me?

55min spaces are gained in 60min. What it is, Can someone explain to me this?

Thank @Ajay.

@Shree.

When hour hand is preceding minute hand then theta=30H~11M/2 will be used otherwise, means when min hand is preceding hour hand then theta=11M/2~30H can be used.

40 * 12/11 = 43 7/11.