Aptitude - Clock - Discussion

Let x be the minute hand.

And x/12 the hour hand.

Since the hour hand moves 5 minutes spaces every 160 minutes.

That means it moves 1 minute space every 12 minutes. And also there are 360 degrees in a clock and 60 minutes.

That means a minute is equal to 6 degrees. It is mentioned that it's 40 minutes after 4.

So, let's first get the distance of the hands in minutes spaces.

= 40-(40/12)+15.

Since the time is after 4 the hour hand is 20 minutes after 12.

= 40-18 1/3.

= 21 2/3.

= 21 2/3 x 6 = 130.

It's 130 degrees apart.

I think the answer should be less than 130 degrees.

Because, here minute hand is at "8" and hour hand is not exactly at "3". The hour hand is slightly shifted past "3". So, slightly reduction in degrees. But not exactly 130 degrees.

Am, I right?

Angle traced in 12 hours = 360 degrees.

Hence for, 3 hours and 40 minutes.

Convert 3 hours into minutes 3 hours* 60 minutes = 180 minutes.

Now, just add 40 minutes with 180 minutes total of 220 minutes.

Now divide 220/60 = 11/3.

At 3:40,

Degree rotated by minute hand 6 deg/min = 40 * 6. ie: 240 deg.

Degree rotated by hour hand 0.5 deg/min = 0.5 * 40. ie: 20 deg + 90 deg (angle between hour hand 3 from 12).

Difference = 240 - (20+90) = 130 deg.

This will bring 140.

The hour hand will be between 3 to 4.
The minute hand will be at 8 because of 40 min.
8-7
7-6
6-5
5-4.

Totally 4*30 =120 degree.
And
Then hour hand will be 40/2 20 degrees.
120 + 20.
=> 140°

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First consider for hours hand.

1hr of hand movement = 30 degrees.

Next for min hand.
5 min of min hand = 30 degrees.

Hence for angle between them subtract the total angle made by them.

3:20.

Formula is((11/2)*M-30(H)).

Here H=3 and M=20.then substitute in formula.

((11/2)*20-30(3)).
((110-90))=20.

The angle in between an hour and minute is 20 degree.

Convert 3hours into min.
60 * 3 = 180.
Then add 40min.
40+180 = 220.

Then 1 hour is equal to 30degre.
30 * 3 = 90.

Then subtract 220 - 90= 130 will be the answer.