Aptitude - Clock - Discussion

Between 4 and 5, the minute hand to move 20 min in right half of circle (watch) from the initial point that is 12 here.

And 30 minutes from 4 in another side to go in opposite direction. So total is 20+30=50.

What does it mean when it says "55 min. spaces are gained"?

As per my calculation, the correct answer will be 55.38 min.

Use this formula:

(5n-30)*12/11 for n>6.
(5n+30)*12/11 for n<6.

How its 55min?

Initially its 12:00am hour and min hand makes 0° after an hour i.e 1:00am hour hand travels 5 min and minute hand travels 60 min so difference between hour and min hand is 55 min.

Use this formula that is Min=60/11 * (Hr+6)

If Hr 1 to 5 make addition
If Hr 6 to 12 make subtraction.

Like Q 4 to 5 clock in opposite directions case

Min = 60/11 * (4+6)
= 60/11 * 10
= 600/11
= 54 6/11. Min. Past.

Its simple just crosscheck each option given, you will get the desired answer like,
for option A:

4:45
4 + 45/60 = 19/4.
360/12 * 19/4 = 285/2°.

And
360/60 * 45 = 270°.

Clearly,
285/2 - 270 = Not equal to 180° (exact opppsite angle) likewise crosscheck all options you will get option D as the right answer.
D:
4 + 600/11 * 1/60 = 54/11°.
360/12*54/11 = 1620/11°.
And
360/60 * 600/11 = 3600/11°.

Then,
3600/11 - 1620/11 = 180° (exact opposite angle).

At 5 O' clock, the minute hand is 25 min spaces behind the hour hand.

Case 1:

The minute hand is 6 min spaces behind of the hour hand.
In this case, the minute hand has to gain (25 - 6) = 19 minutes spaces,
55 min spaces are gained in 60 min, 19 min spaces are gained in [(19/55) * 60] = (20) 8/11 min.

Case 2 :

Minute hand is 6min spaces ahead of the hour hand
In this case, the minute hand has to gain (25 + 6) = 31 minutes spaces
55 min spaces are gained in 60 min, 31 min spaces are gained in [(31/55) * 60] = (33) 9/11 min.

Find the time between 5 and 6 o'clock when the two hands of the clock are 6 minutes spaces apart.

Can anyone help me to solve this?

Why 30-20=10 is not considered as it is done in question number 6?