Aptitude - Clock - Discussion

-> Imagine if both the hands are 12 i.e time is 12:00 then at 1:00 -> Hour hand will be at 1:00 .

-> Minute hand will be at 12 again.Therefore the space gained by minute hand over hour hand is 55 min in 1 hour,i.e. 55 min in 60 min i.e logical data which is used in all problems.

-> Coming to the problem,the hour hand is at 4:00 and minute hand is at 12,therefore to cross hour hand the minute hand has to gain 20 min spaces i.e it means it has to move 20 min forward.

-> Between 4:00 and 5:00 if the hour hand and minute have to be in opposite directions,then hour hand will be at 5:00 and minute hand will be 55 then it has gain 30 minutes more.

-> Totally it has to gain 20+30=50 minutes.

-> If 55->60 then 50->? Ans = 54 6/11 min past 4 they will be in opposite directions.

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.

If we solve by the method of angle difference between hour hand and minute hand, there has to be a difference of 180 degrees for the hands to be opposite.

So I applied this in the equation. If they align 180 degrees opposite to each other after 'x' minutes, then degrees traversed by hour hand will be x*6 and that of hour hand will be (10*4) + (0.5*x).

Taking the difference, the equation formed will be 6x-40-0.5x = 180. Solving this equation gives x=40. So answer should be 40 minutes pas 4.

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).

Hi @Nithya and @Ajit.

"At 4 o'clock, the hands of the watch are 20 min. Spaces apart.

To be in opposite directions, they must be 30 min. Spaces apart.

Minute hand will have to gain 50 min. Spaces".

Are you agree this statement? the same thing "to reach the 5 o'clock in the opposite direction, they must be 30mins. Space apart.

Minute hand will have to gain 55min. Spaces.

(1-2-3-...11) => (5+10+... 55).

So the answer is (60/55) *50 = 54.(6/11).

@Nithya 55 min gained in 60 minutes means.

Suppose its 12:00 am (both the hands of clock have 0 min. difference between them,as they both point towards 12 )then after 60 min(1 hour) hour hand will point to 1, and minute hand will point to 12, now in this position minute hand and hour hand have a difference of 55 minutes between them.

Thats wat he is telling that minute hand gained 55 min in 60 min.

At 4'O clock ---------> 20 mins spaces.

To be in the opposite direction, they must have 30 mins spaces.

So, clock follows the only clockwise direction that's why it has to gain 50 mins spaces apart to be in the opposite direction.

55 mins spaces ----------------> 60 mins.
50 mins spaces---------------> 60/55*50 = 54(6/11)min.

So, the answer is 54(6/11)min past 4.

Assume that they are in opposite directions after x mins..
Then minute hand has traveled x mins...
The hour hand has traveled (x*5)/60 mins from the 4 o' clock position. To this add 20 min to give (x/12)+20 min as its displacement from 12 o' clock...
Now the difference between their positions is 30 mins..
So solve x-((x/12)+20)=30.

Its simple only so i think formula s no need for this ... if both the hands r in opposite direction or in the same straight line in 30 mins spaces ... v have 2 find out the time b\w 4 to 5 . at the time of 4 the spaces b\w the both hand s 20 min so 20+30=50 ...

60/55*50 =54*6/11min past4. hope u will understand?

Its simple only so i think formula s no need for this ... if both the hands r in opposite direction or in the same straight line in 30 mins spaces ... v have 2 find out the time b\w 4 to 5 . at the time of 4 the spaces b\w the both hand s 20 min so 20=30=50 ...
60/55*50 =54*6/11min past4. hope u will understand?