Aptitude - Problems on H.C.F and L.C.M - Discussion

Discussion :: Problems on H.C.F and L.C.M - General Questions (Q.No.3)

3. 

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 D

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).

In 30 minutes, they will toll together 30 + 1 = 16 times.
2


Punk said: (Jul 11, 2010)  
Why 1 is added? please explain.

Sundar said: (Dec 29, 2010)  
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: (Jan 23, 2011)  
Super explanation sundar.

Vishnu said: (Jan 26, 2011)  
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 ?

Mehar said: (Jan 31, 2011)  
WoW...super explanation .thank you:)

Sravanreddypailla said: (Apr 28, 2011)  
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 = 15 tolls(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 15 Tolls + First Toll == 16 dat's it.

Hope you understand.

Sathya said: (Apr 28, 2011)  
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: (Jun 17, 2011)  
Why do you divide 30 by 2?

Ashish said: (Jun 17, 2011)  
Forget about 30/2, look at the answer given by Sravan. 1800/120=15

Thanks Sravan.

Sudha said: (Jun 18, 2011)  
Excellent sravan.

Manju said: (Jul 6, 2011)  
Awesome explaination sravan.

Kundharapu Shravan Reddy said: (Jul 28, 2011)  
Excellent explanation sravanreddy.

Nagaratna said: (Aug 1, 2011)  
@Revathy

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: (Aug 11, 2011)  
Can you please tell me how to calculate LCM of above series no. ? Please tell me.

Deepak said: (Aug 13, 2011)  
@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: (Aug 14, 2011)  
Thank you Sravan I got it.

Gayatri said: (Aug 27, 2011)  
Thank u deepak...

Ali said: (Aug 29, 2011)  
Excellent explanation sravanreddy

Nimmi said: (Sep 28, 2011)  
But why have counted till 120. ?

Rahul said: (Sep 30, 2011)  
Thanks Sravanreddypailla. Its truly good.

Vairam said: (Nov 5, 2011)  
Why 1 is added?

Naveen said: (Nov 12, 2011)  
Really good explnation.

Lakshmisha said: (Nov 24, 2011)  
@Sravanreddypailla, excellent dude...!!!

Sangeeta said: (Dec 2, 2011)  
I didn't understand why did we add 1?

Please explain.

Malatha said: (Dec 8, 2011)  
I also didn't understand why did we add '1'? please tell me.

Balaraju Hari said: (Dec 18, 2011)  
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: (Dec 28, 2011)  
Thanks sundar. Amazing explanation!

Vasu said: (Dec 30, 2011)  
Thanks to both Sravan and Sundar for your explanation.

Fozia Sheikh said: (Jan 11, 2012)  
Four bells toll after intervals of 8, 9, 12and 15minutes, respectively. If they toll together at 3pm. When will they toll together next?

Ramesh said: (Jan 11, 2012)  
Awesome sravan!!

Suparna said: (Jan 12, 2012)  
Why 30 divided by 2 and 1 added?

Divya said: (Feb 10, 2012)  
Please present answer to fozia sheihk.

Manasa said: (Jun 2, 2012)  
120seconds is 2 min so divided by 2.

Saj said: (Jun 15, 2012)  
@Fozia.

I guess the answer should be 9pm, since the LCM of 8, 9, 12, 15 is 360. i.e 360 minutes i.e. after 6 hours.

Yunus said: (Jul 4, 2012)  
One is add because it is clearly given in the question that.

"Six bells commence tolling together" that means all bells rang once than after that rang in intervals of 2 4 6 8 10 and 12.

So add 1 to answer.

Rasheed Tolulope said: (Sep 12, 2012)  
Assuming the tolling follows Arithmetic Progression (AP).
2s, 4s, 6s, 8s, 10s, 12s.
a = 2 and d = 2
In 30 minutes i.e 1800s
Tn = 1800, n = ?
1800 = 2 + (n - 1) 2 = 2 ( 1 + n - 1)
1800 = 2n

n (minutes) = 900s ~ 15 (minutes)

n = 15 times
But note that the six bells started tolling together. Then, plus the first tolling, the number of times they will tolling together in 30 minutes is 16 times

ANSWER = 16 times

Rasheed Tolulope said: (Oct 14, 2012)  
@ Neem.
To find the LCM of 2,4,6,8,10, and 12 using Rasabtol Cross Method (RCM).

2 x 4 x 6 x 8 x 10 x 12 = 2 [1 x 2 x 3 x 4 x 5 x 6]

2 [1 x 3 x 5 x {2 ( 1 x 2 x 3)}]

Apply BODMAS rule,

= 2 [1 x3 x 5 x 2 x 6]

= 2 [1 x 2 x 5 x 3 (1x2)]

= 2 [1 x 2 x 5 x 3 (2)]

= 2 [60]

= 120.
Hence, the LCM = 120

Rahul Vasu said: (Nov 25, 2012)  
LCM method
2 sec, 4 sec, 6 sec, 8 sec, 10 sec, 12 sec = all number is divisible by 2
i.e 1,2,3,4,5,6
= 1x2x3x4x5x6=720
=720/6(bells) = 120 seconds i.e 120/60(seconds) =2 minutes

In 30 minutes, they will toll together = 30/2=15

Since the bells start tolling together, the first toll also needs to be counted. Therefore we need to add 1.

Therefore 15+1=16.

Niharika said: (Jan 25, 2013)  
30/2 in order to calculate time for in fractions to each minute, as the LCM gave 2 minutes as the time.

Kp Mukesh Kumar Singh said: (Apr 28, 2013)  
Superb, it is indispensable for general competition.

Sruthi said: (Sep 19, 2013)  
Why at last 1 has been added?

Mr Perfect said: (Oct 18, 2013)  
Since the bells start tolling together, the first toll also needs to be counted. Therefore we need to add 1.

Kumar said: (Oct 18, 2013)  
It's asked in the question that 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?

Here as per the question the 1st bell can toll 15 times in 30 min i.e (30/2), 2nd bell can toll 7.5 times in 30 min i.e 30/4, 3rd bell 5 times, 4th bell 3.7 times, 5th bell 3 times and 6th one 2.5 times in 30 min...together they tolled 36.7 times in 30 min..

Why this approach is wrong?

Lal Chand said: (Nov 24, 2013)  
Why 30 is divide by 2, please explain?

Veda said: (Jan 29, 2014)  
Well, I will break it into English but no maths.

Generally all the bells rang (toll) at its first encounter, that means all 6 bells started its journey by joining all their hands at once, i.e., at 0th sec<< remember this started journey>>.

Then they lost their hands and joined again at 120th second, in the mean-while they are tolling individually and not combinedly.

1. It is nothing but at 14th 19th. 25th 38th 57th 69th. Until 119th sec they didn't rang combinedly then at *120th* sec they combined their hands and rung. This is the least number that those 6 bells have waited for their combined toll (nothing but LCM in maths criteria), shortcut used.

2. Then they again rung combinedly after *120*+120th=240th sec+. 120+120+..until 1800.

3. They had given us 30min =1800 sec) , so if we divide that 1800 sec by 120sec (intervals) 1800/120=15 we will get.

Actually this (15) should be the answer if all the bells did not start combinedly, but our bad luck, they mentioned in the question that ""Six bells commence tolling together. "" that means they have started its journey itself by ringing combinedly.

4. The extra +1 is nothing but this started journey.

Now go through what @Saravan and all others said you will get more detailed idea.

Hope this understands. Thank you.

Dushanthi said: (Feb 24, 2014)  
Why we find the L.C.M.?

I can't understand the L.C.M. method. What is the difference between L.C.M and H.C.M. Why didn't use the H.C.M. method in here. Please anyone can explain me.

Prem said: (May 15, 2014)  
I am unable to understand why we are using lcm method for this problem. Can anyone explain?

Atishay said: (Jul 19, 2014)  
Why not using HCM:

Suppose 3 bells are tolling at 2, 4, 6 sec,

HCM is 2, so now think, is it possible that they will toll at every 2 sec. NO.

We will have to find a common number (multiple) which is occurring to every bell and that is called LCM.

So LCM here is 12.

That means every bell will toll at 12th second.

Nakum Paras said: (Oct 16, 2014)  
Actually got solution.

All bells starting from 1 second at a time 1 time bells tolling at a time.

1st bell tolling every 2 sec means 2, 4, 6, 8,...120...240... 360....480

2nd bell tolling every 4 sec means 4, 8, 12, 16...120...240...360...480

3rd bell tolling every 6 sec means 6, 12, 18, 24...120...240...360...480

4th bell tolling every 8 sec means 8, 16, 24...120...240...360...480

5th bell tolling every 10 sec means 10, 20, 30...120...240...360...480

6th bell tolling every 6 sec means 12, 24, 36...120...240...360...480

So 1 sec =1 time tolling at a time.

120 sec = 2 time tolling at a time.

240 sec = 3 time tolling at a time.

360 sec = 4 time tolling at a time.

4800 sec = 5 time tolling.

600 sec = 6 time tolling at a time.
.
.
Last 1800 sec = 16 time tolling at a time.

Total time bells tolling at a time =16 times.

Rohan Bhoir said: (Oct 20, 2014)  
Can you tel me how is the HCM can find? Explain with any example.

Pri said: (Nov 9, 2014)  
Please explain me HCM. I can't get clear idea about it.

Upendra said: (Jun 3, 2015)  
Why 1 added?

Saikiran said: (Jun 17, 2015)  
Six bells commence tolling together means six bells started tolling together that's why 1 is added to 15, now 15+1=16.

Commence=Start or begin.

Sumit Chauhan said: (Jul 3, 2015)  
But why are we add 1? Because when we toll together all the ball. They toll together. And that time also count in first 30 min.

Divi said: (Jul 6, 2015)  
Very clear explanation. Thank you.

Shrinivasmutagar said: (Jul 23, 2015)  
Why that 120 sec have been took?

Mahesh said: (Aug 21, 2015)  
How do you get that 120?

Gowthami said: (Aug 30, 2015)  
As they all together, why should we add 1, I couldn't understand. Why will first bell toll first, it starts together with the 5 bells know?

Akhil said: (Sep 2, 2015)  
4 bells ring at an interval of 12, 16, 20, 24 min if they start together at 9 am after how long will they ring together.

Sam said: (Sep 7, 2015)  
12 = 2*2*3.

16 = 2*2*2*2.

20 = 2*2*5.

24 = 3*2*2*2.

L.C.M = 2*2*2*2*3*5 = 240 min.

= 240 min/60 min = 4 hr.

So at 1 pm it will ring again (9+4).

Anand Jannu said: (Sep 17, 2015)  
@Saravan explained excellent. But that concept 30/2+1 I didn't understand. But I follow concept said by @Saravan.

Awanish said: (Oct 20, 2015)  
I am not agree with this explanation 1st beep at 0 sec so time start after 0 so within 30 min it beeps 15 times.

For 16 beep it takes 30 min 1 sec.

Renuka said: (Oct 20, 2015)  
Really it is a good explanation. Thanks.

Secotad said: (Oct 30, 2015)  
The bells toll at Intervals of 10mins, 15mins, 20mins. If they toll together at 11:00am, when next do they toll again.

Secotad said: (Oct 30, 2015)  
The bells toll at Intervals of 10mins, 15mins, 20mins. If they toll together at 11:00am, when next do they toll again.

Muneesh said: (Dec 12, 2015)  
Formula: (n/2+1) from n--30.

= 30/2+1 = 16 answer.

Dhivakar said: (Feb 22, 2016)  
If all the bells starts to toll, it will get the toll together only at the 120th second. If a bell starts to tell, will it start from zero or directly from 120?

Simi said: (Mar 22, 2016)  
Answer for Fozia Sheikh 21:01 P.M.

Lalit Salaria said: (Apr 3, 2016)  
LCM of 10, 15, 20 = 60 minutes = 1 hour.
Thus, bells will toll after 1 hour.

Thus 1:00 pm is the answer.

Lalit Salaria said: (Apr 3, 2016)  
Can anyone answer for Secotad question?

Raman said: (Apr 10, 2016)  
Very good explanation @Sravanreddy.

Rinkz said: (May 18, 2016)  
Thanks, all of you solvers. It's really useful.

Bala said: (Jun 14, 2016)  
Can anyone explain for Awanish's answer because time starts after 0? Also, I have another sum. A train travels 10days daily. B train travels 10days daily but opposite to A. If a man in A starts 11 am and reaches other station after 10days how many B trains he had passed if starting the train of A = starting time of B ie. , 11 am, thanks.

Nand said: (Jun 15, 2016)  
Can anyone please help me out getting the answer of the below question.

The bells commence tolling together & they toll after 0.25, 0.1 & 0.125 seconds. After what interval will they again toll together?

Nand said: (Jun 15, 2016)  
I hope 16 is not correct, as the question is simply saying how many time the bells will toll together in 30 mins.

We got that they will toll together in every 2 mins so 0-2, 2-4, 4-6, 6-8, 8-10, 10-12, 12-14, 14-16, 16-18, 18-20, 20-22, 22-24, 24-26, 26-28, 28-30.

So seems the answer is 15, if wrong please rectify me.

Anonymous said: (Jul 4, 2016)  
Friends, Let bells ring together once in 120 seconds.
Let's say they all ring for the first time at 1st sec and they ring altogether once again after 120 sec, say 121st sec.

Therefore they ring at.

1st sec, 121st sec, 241st sec, and this series forms an ap with.

A = 1, d = 120.

Therefore.
Number of terms before 1800 =1 6 (should be) as per answer given.

But the number of terms comes as 15 and the bells ring together at 1801st sec for the 16th time.

Anare.Vadei said: (Jul 5, 2016)  
Why use 120 seconds? What does it represent?

Nanuram Jamra said: (Jul 14, 2016)  
As per my calculation, the correct answer is 15.

Sahil said: (Jul 17, 2016)  
@Anare: it represents that after every 120sec bells toll together.

Shanmathi said: (Jul 23, 2016)  
Nice post @Sundar.

Kinjal said: (Jul 28, 2016)  
Nice Explanation @Sravanreddypailla.

Kalyan said: (Aug 3, 2016)  
Thanks @Sundar.

Lahu said: (Aug 17, 2016)  
@Balaraju Hari.

It is Awesome, Thanks for your explanation.

Salman Pasha said: (Aug 18, 2016)  
But why we should divide episode by 2 (120 sec)?

K.Gayathri said: (Aug 27, 2016)  
What is mean by toll?

Divyansh said: (Sep 1, 2016)  
Can anyone please say it Ring or Start ringing?

Divyansh said: (Sep 1, 2016)  
Because of all bells ring/toll together after every 2 min (120 s). So to find that how many times all bells tolled together in 30 mins we need to divide the episode i.e. 30 mins by 2 min (120 s).

At last, we add 1 because we have to count all the number of times the bells tolled together in 30 mins, as they started tolling together so their first toll also needs to be counted and hence we add 1 in 15 and get the answer as 16.

Mahagopi said: (Sep 1, 2016)  
Thanks for your explanation.

Bahhep said: (Sep 19, 2016)  
In 30th min they meet together but they don't toil together. So it should be 15 not 16.

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