Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
[A].
4
[B].
10
[C].
15
[D].
16
Answer: Option C
Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120.
So, the bells will toll together after every 120 seconds(2 minutes).
If two bells toll after every 3 secs and 4 secs respectively and if they commence tolling at the same time.
then the first bell tolls after every 3, 6, 9, 12 secs...
the second bell tolls after every 4, 8, 12, ....
So they toll together again after 12 secs, which is the LCM
Henceforth they toll after every 12 seconds, i.e whenever the time is a common multiple of both 3 and 4.
Since the bells start tolling together, the first toll also needs to be counted. Therefore we need to add 1.
Kushal said:
(Sun, Jan 23, 2011 05:55:33 AM)
Super explanation sundar.
Vishnu said:
(Wed, Jan 26, 2011 01:52:08 AM)
So We need to count that first commence according to your answer.
But according to the question we need to find the time after first tolling together na ?
Commense is nothing but start tolling. here six bells are there and toll together at intervals 2,4,6,8,10,12
first bell tolls at every :2secs,4secs,6sec......120sec....
second bell tolls at every :4secs,8secs,12secs.....120secs.....
third bell tolls together at every:6sec,12sec,18sec..120sec...
fourth bell tolls together at every:8sec,16sec,24sec...120sec..
fifth bell tolls together at every:10sec,20sec,30sec ,....120sec...
sixth ell tolls together at every:12sec,24sec,36sec....120sec...
NOW OBSERVE ALL TOLLS the common sec in *All* bell tolls is 120sec
thats why we need to find l.c.m in shortcut
come to question:
1 toll altogether takes time=120sec
? tolls altogether takes time=1800sec(30min*60sec)
the number of tolls are 1800*1/120=15tolls(times)
but in question:
Six bells commence tolling together(first toll) and also toll at intervals of 2, 4, 6, 8 10 and 12 beginning itself started from tollinf so we should consider that toll also
hence answer is 15tolls+firsttoll==16 dat's it
hope u understand
Sathya said:
(Thu, Apr 28, 2011 10:07:57 AM)
Excellent sravan now I understand everything in the question n wt you said. Its really very helpful to me. , AND YOUR EXPLANATION IS VERY VERY CLEAR.
THAN YOU VERY MUCH sravan!
Revathy said:
(Fri, Jun 17, 2011 04:13:04 AM)
Why do you divide 30 by 2?
Ashish said:
(Fri, Jun 17, 2011 11:38:26 AM)
Forget about 30/2, look at the answer given by Sravan. 1800/120=15
At first time all bells toll together at 120sec (i.e, 2 minutes).
But not only at 2 mins they toll together at multiples of 2mins they toll together. That means at 2min, 4min, 6min...........30min, 32,34,..........That is they continue the same.
But they have asked to find tolling only upto 30mins. So now if you divide 30min by 2 you will get 15.
Neem said:
(Thu, Aug 11, 2011 12:36:51 AM)
Can you please tell me how to calculate LCM of above series no. ? Please tell me.
Deepak said:
(Sat, Aug 13, 2011 02:37:08 PM)
@neem
2=2
4=2*2
6=2*3
8=2*2*2
10=5*2
12=2*2*3
nw select d max count for 2 3 5
for 2. Its in 8. I.e. 2*2*2.
Then 5 n 3 are only once in any combination.
So lcm=2*2*2*3*5=120
Krishna said:
(Sun, Aug 14, 2011 12:53:56 AM)
Thank you Sravan I got it.
Gayatri said:
(Sat, Aug 27, 2011 11:17:03 AM)
Thank u deepak...
Ali said:
(Mon, Aug 29, 2011 06:52:09 AM)
Excellent explanation sravanreddy
Nimmi said:
(Wed, Sep 28, 2011 05:39:56 PM)
But why have counted till 120. ?
Rahul said:
(Fri, Sep 30, 2011 09:34:23 PM)
Thanks Sravanreddypailla. Its truly good.
Vairam said:
(Sat, Nov 5, 2011 09:55:06 AM)
Why 1 is added?
Naveen said:
(Sat, Nov 12, 2011 11:17:59 PM)
Really good explnation.
Lakshmisha said:
(Thu, Nov 24, 2011 09:19:03 PM)
@Sravanreddypailla, excellent dude...!!!
Sangeeta said:
(Fri, Dec 2, 2011 08:42:04 AM)
I didn't understand why did we add 1?
Please explain.
Malatha said:
(Thu, Dec 8, 2011 12:17:10 PM)
I also didn't understand why did we add '1'? please tell me.
Balaraju Hari said:
(Sun, Dec 18, 2011 04:10:39 PM)
Its simple, according to the shortcut formula everyone understood why the tolling together takes place at every 120sec(2min) period from the l.c.m concept.
But why 1 is added means, it is clearly mentioned in the question that the 6 bells starts tolling together at the starting stage(first tolling is done by together) and tolls at the intervals 2, 4, 6 ,8, 10, 12. so, before tolling together at 120sec(2min), they already tolls together at the 1st(zeroeth sec i.e starting) itself. so that 1 is added.
Aashish said:
(Wed, Dec 28, 2011 09:28:10 PM)
Thanks sundar. Amazing explanation!
Vasu said:
(Fri, Dec 30, 2011 08:59:07 PM)
Thanks to both Sravan and Sundar for your explanation.
Fozia Sheikh said:
(Wed, Jan 11, 2012 02:34:01 AM)
Four bells toll after intervals of 8, 9, 12and 15minutes, respectively. If they toll together at 3pm. When will they toll together next?
