Aptitude - Clock - Discussion

@Rajvee 5:55 is wrong, so only 11 times in 12 hours (opposite direction).

If it coincides 22 times in 12 hrs and 22 in next 12. Then where is in between time. Means 44 + 1 = 45 should be there.

@All.

Hi, I am 76 years old and this is quite simple, but you have made it difficult.

First, the problem statement could be made clearer; however, taken as stated is reasonable, but the grammar is incorrect. Corrected problem statement: " How many times in a day are the hands of a clock in a straight line?"

Solution: (Hands on, not algebraic, but algebra works too). Get a standard clock with dials and point the hour hand and minute hand at 12. Then, proceed to dial the minute hand around until it is in a straight line with the hour hand. That's "1" Continue turning the minute hand until it aligns with the hour hand (they are in a straight line).

That's "2" Continue until you have hand alignment at the 6 on the clock. At this point, you will have "11" instances of the hands being in a straight line. That is 6 hours. In 24 hours, the number of instances of the hands being in a straight line is "44."

Initially hours hand, minutes hand and second hand are in overlapping condition so, the counting is started from 1:35 then 2:40 then 3:45....... 11:25. ( straight line is started from 1:35 to 11:25). from this counting, we get only 11 times in 12 hours.

Mathematically,
For 1 hours, minutes hand travel 60 min and hours hand move only 5 min that means hours hand loss 5 min that means hours hand travel 55 min.

So, when hours hand travel 55 min minutes hand travel 60 min.
1 ,, ,, ,, ,, ,, ,, (60/55).
30 ,, ,,, ,, ,,(60/55) * 30 = (360/11).
[ in straight line condition, minutes hand should 30 min apart from hours hand].
[ hand will be straight 2 times in hours].

So, in 1 hours minutes hand travel (360/11) * 2 = 720/11.

In 24 hours, {(24 * 60)/(720/11)} = 22 times.

Thank you to all for the solution.

Thank you all for the explanation.

What about, Hour hand on 12-minute hand on 6 then hour hand on 12 plus 1 minute and the minute hand on 6 plus 1?

It maybe equals 29 in 12 hours x 2 equals 58.

22 hours is the answer.

In 1hr the minute hand rotate 60 min, and the hour hand rotate 5 min.

So 1 hr hour hand rotate 5 min.

24 hr hour hand rotate 24*5=120, that means (60+60) min=2 hr.

Hence 24-2=22 hr and you know that every hour the min hand and hour hand become straight.

So it is clear that answer is 22 hr.

The Correct Answer is 22.