Aptitude - Clock - Discussion

I think straight= coincide+ opposide.

So, we got 44.

I think the correct answer is 22.

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.

22 hours is the answer.

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.

Thank you all for the explanation.

Thank you to all for the solution.

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.

@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."

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