Aptitude - Clock - Discussion

@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?

@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!

There is a formula for finding time nd degree
ie angle=(11/2)*min-30*hr
in this problem the hr nd min hands should be in right angle that means angle=90 then we can find min
90=(11/2)*min-30*5
min=(90+150)*(2/11)
=43 7/11 ie 5hrs 43 7/11min

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.

@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.

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

40 * 12/11 = 43 7/11.

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.

If the hours are less than 6 or the angle less than 180 then use...theta =11/2(min)-30(hrs).

If the hours are greater than 6 or the angle greater than or equal to 180 then use...theta = 30(hrs)-11/2(min).

It's simple and helps a lot. Good luck.

At 5:30, the hands are 55 mins apart.To get an angle 90 btw them space must 15 mins apart,

so, the space is 55-15=40.
therefore,60/55-40=43 7/11.