Aptitude - Problems on H.C.F and L.C.M - Discussion
Discussion Forum : 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 ?
Answer: Option
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 |
Discussion:
170 comments Page 2 of 17.
Divyansh said:
9 years ago
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.
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.
RASHEED TOLULOPE said:
1 decade ago
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
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
Chojoy said:
6 years ago
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.
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.
(2)
Nagaratna said:
1 decade ago
@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.
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.
Rahul Vasu said:
1 decade ago
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.
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.
Sagar said:
7 years ago
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.
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.
(2)
Bala said:
9 years ago
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.
Misbah said:
8 years ago
Take a look to the question as it starts with 'six bells commence tolling together' that means they have already tolled for once and they are doing together every two minutes. In 30 seconds, they will toll for 15 times and we have to count the one they did at the beginning. So in 30 minutes they will toll for 16 times :).
Nand said:
9 years ago
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.
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.
Atishay said:
1 decade ago
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.
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.
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