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 4 of 17.
Suparna said:
1 decade ago
Why 30 divided by 2 and 1 added?
Divya said:
1 decade ago
Please present answer to fozia sheihk.
Manasa said:
1 decade ago
120seconds is 2 min so divided by 2.
Saj said:
1 decade ago
@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.
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:
1 decade ago
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.
"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:
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
Rasheed Tolulope said:
1 decade ago
@ 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
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:
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.
Niharika said:
1 decade ago
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:
1 decade ago
Superb, it is indispensable for general competition.
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