Question

Three bells toll every 30 min, 45min, and 60min. if they toll together at 9:30am, what is the next time they will toll together? ticka 10pm tickb 11:45pm tickc 12:30pm tickd 1:45 pm

Answer 1

Solution:

We have to find the L.C.M of 30,45,60

30 =2× 5×3

45= 3 x 3×5

60 =2× 2× 3 x 5

L.c.m ( 30,45,60) = 2x2x3×3×5 = 180 min

= 180 /60 = 3 hours.


Hence,they will toll together at = 9:30 a.m +3 hrs= 12:30 p.m

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Hope this will help you...

Answer 2

Time duration between successive tolls of each bell:
          30 min, 45 min, 60 min...

All tolled at 9:30 AM together.

Bell1 will ring after 30min, 60min, 90min, 120 min, 150min, 180min...
Bell2 rings after 45min, 90min, 135min, 180min, 225min, 270min...
Bell3 rings after 60min, 120min, 180min, 240min ...

So all three ring together after 180 min or 3 hours.  ie., at 12:30PM

The duration between successive tolling of all bells together is found by finding the LCM of the three time durations.

  30 = 2*3*5
  45 = 3*3*5
  60 = 2*2*3*5
LCM = 2*2*3*3*5 = 180 min

So after 3 hours. ie., at 12:30pm
That is the answer.