Aptitude - Clock - Discussion

I agree with the Mamta's Explanation. Thanks @Mamta.

At a railway station, a 24-hour watch loses 3 min in 4 hours. If it is set correctly on Sunday noon when will the watch show correct time?

Please give me the solution.

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.

Yes, I too think the Right answer is option A.

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.

Given in question that in every 3 minutes 5 sec = 185 sec. increases, so the wrong time we get 4:15.

Now we have to get the correct time, for this first take the wrong time.
Given it is 4:15 which is started from 7 in morning, so that's mean it is 9 hr 15 minutes.
555 min = 333000 sec.
Now for the correct clock,
It will be 3 minute = 180 seconds.

So, correct time can be written as (180/185)*333000 sec. = 32400 sec.
which is equal to 9 hr so the answer is 4 p.m.

Anyone can tell 4.15 PM so how can you say 15 min the question is only 4?

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

From 7am to 4:15pm it takes 9hrs15mins. But for ever 3mins the secs hand moves 5secs extra so so 9hrs15mins =x (3+ (5/60))because 1sec=1/60 so5secs=5/60. X=540mins. 540mins=9hrs so 9hrs from 7am is 4pm.

7am to 4.15pm.
Total 9hrs 15min.

Total time in min= 9*60+15=555min.
For every three min, 5 seconds will be added to the wrong clock
555min /3min= 185 times

So total second added 185*5=925sec,
now convert 925sec to min=925/60= 15 min 25 sec,
so the time in original clock will be 4pm.
555min-15min, =540min=9hrs.
25 sec is neglected because clocks trigger by 5sec only after completing 3mins.