Aptitude - Clock - Discussion

Discussion Forum : Clock - General Questions (Q.No. 15)
15.
At what time between 9 and 10 o'clock will the hands of a watch be together?
45 min. past 9
50 min. past 9
49 1 min. past 9
11
48 2 min. past 9
11
Answer: Option
Explanation:

To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.

55 min. spaces gained in 60 min.

45 min. spaces are gained in 60 x 45 min or 49 1 min.
55 11

The hands are together at 49 1 min. past 9.
11

Discussion:
48 comments Page 4 of 5.

Niki said:   1 decade ago
@Gaurav Mittal.

How you counted moves for minute hand ? i.e. You took 6x. How? Can you please explain?

Gaurav Mittal said:   1 decade ago
Friends.

We know that the hour and the minute hand will coincide somewhere between 9 and 10. At 9:45, the angle between the hour & the minute hand is 22.5 degrees (the hour hand gains 0.5 degree per minute, i.e. 45/2 degrees in 45 mins).

Now, assume that the minute and the hour hand coincide at x mins after 9:45.

So, in x mins, the hour hand moves x/2 degrees while the minute hand moves 6x degrees.

So, 6x - x/2 = 22.5 (i.e. from the original position to the new position)

So, x = 45/11 = 4 1/11.

So, the time at their meeting is 49 1/11.

Goku said:   1 decade ago
Keep it simple friends! Just use this formula.

12/11 (minutes to be gained). See in the question between 9 to 10'o clock we know that at 9:45 the hands will coincide so 45 minutes is to be gained from 9 o'clock.

So 12/11* (45) =49 1/9 (Answer).

$hr!dhar said:   1 decade ago
@Shree Hema: Hats Off To u!!! Awsm Formula!!
thnks ;)

can u plz give derivation of formula...

Nivesh said:   1 decade ago
Thanks Kapil you have explained it in a very basic manner.

Kapil said:   1 decade ago
It's very simple..

in 12 hour a hour hand gains angle= 360 degree
so in one hour it will gain = 360/12 = 30 degree

similarly,

in 60 minutes a minute hand gains = 360 degree
so in 1 minute it will gain = 360/60= 6 degree

so angle gain by hour hand at any time = 30*[y+(x/60)] degree
& angle gain by minute hand=6*x degree

where y=no. of hour (in this question it is '9')
&
x=minutes after the y O' clock..

angle gained by hour hand should be Equuleus to minute hand..

=> 30*[9+(x/60)]=x*6
=> 270+ x/2=6x
=> 540+ x=12x
=> 11x= 540
=> x= 49 1/11

Jasraj khatri said:   1 decade ago
When minute hand reach to 9, hour hand reach near to 10. Then why you count 45 spaces?

Pradeep said:   1 decade ago
Here we can use the formula:
theta=11(m)/2-30(h)
same direction means 0 degree; hour=9
180=11(m)/2-30(9)
m=49 1/11

Anil said:   1 decade ago
If time is between x and y:

[x*5+angle]*(12/11) past x.

Senthamizh said:   1 decade ago
@Shree: is that standard formula???


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