Aptitude - Clock - Discussion

@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."

in this Question u give the explanation like:
. How many times in a day, the hands of a clock are straight?

A. 22 B. 24
C. 44
D. 48

Answer & ExplanationAnswer: Option C

Explanation:


In 12 hours, the hands coincide or are in opposite direction 22 times.

In 24 hours, the hands coincide or are in opposite direction 44 times a day.



AND

This is also the same Question

How many times in a day, are the hands of a clock in straight line but opposite in direction?

A. 20 B. 22

C. 24 D. 48

Answer & ExplanationAnswer: Option B

Explanation:


The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).

So, in a day, the hands point in the opposite directions 22 times.



So,how the answera is different? Let me Explain plz.

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.

@Krishnamurthy

It is very simple if you know difference between statements
"straight" and "straight line but opposite in direction"

(a)if statement is "straight" then answer is = 44.
(hands will be straight 2 times in hour,when they are opposite
and second when they coincide)

(b)if statement is "straight line but opposite in
direction" then answer is = 22.
(hands will be straight but opposite once in hour)

From morning to noon, 12:30 1:35 2:40 3:45 4:50 5:55 6:00 7:05 8:10 9:15 10:20 11:25 (in opposite direction) and 1:05 2:10 3:15 4:20 5:25 6:30 7:35 8:40 9:45 10:50 11:55 12:00 (when coincides)

Now from noon to night, 12:30 1:35 2:40 3:45 4:50 5:55 6:00 7:05 8:10 9:15 10:20 11:25 (in opposite direction)

1:05 -----*** 12:05 (when coincides)

It's 48 times.

How is it 44?

It's 44 only. All explanations given are correct. What they have asked is how many times the hands will be straight. So the hands make 0 deg 22 times a day and 180deg 22 times a day. Since they have asked the addition of both the situations the answer will become 44.

Hope you understood whats being asked and how the answer is 44 by my explanation, cheers.

17th answer: The hands of a clock coincide 11 times in every 12 hours means 22 times per day(Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).

18th answer: In 12 hours, the hands coincide (or) are in opposite direction 22 times.

Which one is right for the hands of a clock to be coincide?

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.

Even I have the same doubt @Rajveer.

That the answer should be 48 because in 12 hrs the hands are opposite in direction 4 at 24 times, not 22 times. So that means in 24 hrs the hands must be in oppsoite direction 4 at 48 times rather than 44 times.

@ krishna murthy and Nitesh Nandawa - The correct answer is 22 times, the hands of a clock neither coincide nor come in a straight line 44 times in 24 hours, they just come 22 times in 24 hours that is 11 times in 12 hours.
22 is the right answer.