Aptitude - Clock - Discussion

@All

| 5.5X - 5*30 | = 90.

5.5X - 5 * 30 = +90 and 5.5X - 5 * 30 = -90.

By solving this we will get both the answers where at 5'o clock at which they make 90deg angle.

Hope this helps!

5’o clock, space between the hour and min 25 min.
1 hr hand =30 degree.

5:30 and 6 will hands (30 min) of the clock 15 degrees.
So now total 5’o + 5:30 = 25 + 15 = 40min.

Now we know that 55 min space is gained in 60 min.
Then 40 min space are gained =(55/60) * 40 min.
43(7/11) min,
So, the Required time 43(7/11) min .past 5.

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.