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?

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

@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!

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

@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.

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.

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.

@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.

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.