Aptitude - Clock - Discussion

Time between 7AM to 4.15PM = 9 hours 15 Minutes = 9+15/60 hours = 9+1/4 hours = ((9*4)+1)/4 hours = (36+1)/4 hours = 37/4 hours.

Now 3 Minutes 5 seconds of this clock = 3 minutes of the correct clock--------(1).

So, by converting above into hours we get,
First we convert into minutes,

3+5/60 = 3+1/12 = ((3*12)+1)/12 = 37/12 ---------(2).

Now we convert above result into Hours, we get 37/12*60 = 37/720 hours.

And on right side of equation 1, 3 minutes after converting into hours becomes 3/60 hours that is 1/20 hours----------(3).

So from equations 1, 2, 3 we get,
37/720 hours of this clock = 1/20 hours of correct clock.

Then 37/4 hours of this clock = (1/20)*(37/4)*(720/37) = 9 hours.
Therefore correct time is 7+9 hours = 16 Hours on 24 clock, that is 4PM on 12 hours clock.

Another view can be:

In 3 minutes the error is 5 seconds, so every hour it gains 100 seconds.

Correct Clock ----------------------------> Wrong Clock
7 hrs ----------------------------> 7 hrs
8 hrs ----------------------------> 8hrs 100 sec
9 hrs ----------------------------> 9 hrs 200 sec
10 hrs ----------------------------> 10 hrs 300 sec
11 hrs ----------------------------> 11 hrs 400 sec
12 hrs ----------------------------> 12 hrs 500 sec
1 hrs ----------------------------> 1 hrs 600 sec
2 hrs ----------------------------> 2 hrs 700 sec
3 hrs ----------------------------> 3 hrs 800 sec
4 hrs ----------------------------> 4 hrs 900 sec ----> 4 hrs 15 minutes

To: Nitin

You are wrong. The given answer is correct. Don't get confused.

Let me explain in simple manner:

Error Clock :: Original Clock

3 min 5 sec :: 3 min

185 sec :: 180 sec

[9 hr 15 min = 555 min = 33300 sec]

33300 sec :: (180/185 x 33300) sec

33300 sec :: 32400 sec

333000sec = 9 hrs 15 min :: 32400 sec = 9 hrs [:. 32400/3600 = 9]

So,
Time passed by Error clock = 9 hrs 15 min.
Time passed by Original clock = 9 hrs.

Therefore, 9 hrs after 7 am is 4 pm.


Note: What was wrong in Nitin's explanation?

555/3 <--- Problem is here.

It should be

555 min/3 min 5 sec [or] 33300/185

Please think twice before solve problem. Hope this will help you. All the best!

Option A is the right answer.

Explanation: for every 3 minutes its gaining 5 seconds.
3 min = 5 sec ------------------(1)
So in 1 hour it will gain.
(60 min * 5 sec) / 3 min = 100 sec-------------(2)
So in 9 hours( 7 a.m. to 4 p.m) it will gain.
(100 sec * 9 hrs) = 900 sec---------------------(3)
In 15 min it will gain (15 min * 5 sec) / 3 min= 25 sec------------(4)
Total in 9 hours 15 min( 7 am to 4:15pm) it will gain = 925sec.
Now convert 925 seconds into minutes.
i.e, 925/60 = 15.416667 (this is not a approximation problem. We cannot neglect the numbers
After decimal point) = 185/12 = 15 5/12.
So now, 4:15 -(minus)15 5/12 = 3:59:35 = 59 7/12 past 3 pm.

It's given that error clock gains 5 seconds in each 3 minutes of perfect clock.
So, 3min 5sec of error clock = 3min of perfect clock.

Or, [3+(5/60)] min of error clock = 3min of perfect clock. (185s of error clock = 180s perfect clock)
Or, (37/12) min of error clock = 3min of perfect clock
Or 1 min of error clock = 3*12/37 min of perfect clock =36/37.

Now error clock moved from 7am to 4:15pm = 9hr 15min = ( 9*60 + 15 )min = 555min.
So in 555 min of error clock = (36/37)*555 min of perfect clock = 540min of perfect clock.
= (540/60) hr = 9 hr of perfect clock.
So 9hr from 7am is 4pm. Thus the answer is [B] 4 p.m.

@Manisha.

I hope this will help you.

5 sec gained in 3 min, so,convert 3 min into 1 hr (for convenience).

(5*20)sec gained in (3*20)min.
100 sec gained in 1 hr (60 min=1 hr).
The total duration b/w 7 am to 4.15 pm = 9.15 (9 hr 15 min).

(15 min = 1/4 hr) so, 9.15 = 9 hr + 1/4 hr = 37/4 hrs.

In 1 hr 100 sec gained so, in 37/4 hrs ?
(37/4)*100 = 37*25 = 925 sec.

Convert sec into min:
925 sec = 925/60 min = 15.41 min (approx 15 min).

True time calculation:

Time is to be gained so, clock running fast. To find the true time , we need to subtract 15 min from 4.15.

Then, true time = 4.15 - 15 min = 4 pm.

It gains 5 seconds in 3 minutes.

3min = 5seconds
3min = 1/12 min
1min = 1/36 min

Let correct watch shows time which is x min ahead of 7 am.

Then minutes gained by faulty clock = x/36minutes.

So, the faulty clock is ahead of 7 am by (x + x/36)min or 37x/36 min.

but in question, it is given faulty clock shows 4.15 pm which is (9*60+15)min or 555min ahead of 7 am.

So,
37x/36 = 555

x = 540min or 9 hrs

So, the correct time is 7 am + 9hr = 4 pm.

Note: We have to calculate the time gained by the faulty clock in terms of the correct clock not in terms of the faulty clock time given in the question

The problem is with the calculation of 9hr 15min=555 minutes. This value is associated with the erroneous clock. You need to convert it for the true clock. As per data, we can write,

3 mins in the true clock equals 3 min 5 seconds (3+5/60 or 37/12 minutes) in erroneous clock. Thus we have

37/12 mins of erroneous clock equals 3 mins of true clock.
1 mins of erroneous clock equals (3*12/37) mins of true clock.
555 mins of erroneous clock equals (3*12*555/37)=540 mins of true clock.

540 minutes = 540/60 hours = 9 hours. The actual time is (7+9) hours = 16 hours = 4P.M.

Consider the ratio of the speed of original clock : error clock;.

By the time original clock covers 180 secs, error clock covers 185 secs.
therefore speed ratio is 180(original) : 185 (error).
==> 36:37.
Error clock covers 9 hours 15 mins= 9 1/4 hours = 37/4 hours.
Now solving by ratio proportion,

Speed --- time covered(in hours)
37 --- 37/4 ---------> Error clock
36 --- ? ---------> Original clock

Time covered by original clock is ==> 37/4 * 36/37.
==>9 hours i.e, clock shows at 4.00 pm.

In 3 MIN = The clock gains 5 sec.
in 60 min(3 * 20) = clock gains 100 sec(5 * 20)
= i.e 100/60 min
= 5/3 min
So , If correct clock shows 1 hour=den da wrong clock shows 1 hr 5/3 min..
i.e
1 hr=1 hr 5/3 min
=1 * 5/(3*60) hour (convert to hour)
=37/36 hour

But we need to do reverse..
i.e
37/36 hrs(in wrong clock) = 1 hr
1 hour in wrong clock = 1/(37/36)=36/37 hr

9hr 15min=37/4 hrs

So
37/4 hours in wrong clock =36/37 * 37/4
= 9
So 7 a.m + 9 hrs= 4 pm ....

I hope every1 got it...