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

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.

As it is clear from the question and the answer provided that the bells Are going to toll together after every 2 min.

So, in the given interval of 30 min.

They will be going to toll 30/2 that is 15 times and early in the question they have mentioned that the bells are already toll together at once.

So, the answer is 30/2 + 1= 16 times.

You can also use AP(Arithmetic Progression) method to solve this problem.

Since the given tolling interval are in AP,ie 2 4 6 8 10 12........ , and nth time is 30min.

HENCE, using AP formula, we have;
T(N)=a+(n-1)d
a=2, d=4-2 ie d=2, n=?
30=2+(n-1)2
30=2+2n-2
ie, 30=2n
therefore, n=15.

Since we have to consider first toll, add+1 to n.
Therefore, the answer is 15+1=16.

Why do you divide 30 by 2?

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.

Why 1 is added your answer in the question. Read it once again carefully.

@Kyra.

Here, it is asked in 30 minutes how many times 6 ring balls roll together.

6 ring balls roll every 2 minutes
So, we divided for 30 minutes how many 2-interval exist.

Why 1 is added? please explain.

Super explanation sundar.

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 ?