Six Bells

Number Theory Level 3

Six bells, commencing tolling together, toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

16 30 12 15

Tan T by Tan T , 27, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tan T
May 25, 2016

we start by taking the LCM(Lowest common multiple) of their given respective times. hence the LCM will be that interval of time after which they toll together. the LCM of 2,4,6,8,10,12 is 120 (seconds) i.e, 2 minutes hence in 30 minutes they will toll 30/2 =15 times plus the additional first tolling at commencement. hence answer is 15+1=16 times

4 Helpful 0 Interesting 0 Brilliant 0 Confused

But if the question is strictly limited to thirty minutes, and ends at the commencement of second number 1800, then that final synchronized chime will occur after end-time. Either that or the initial sync chime should be too early. Can't have both. Answer should be 15.

David Miller - 4 years, 11 months ago

they commence together. that is not counted in the other 15 times they toll together. and the last time they toll together is the 15th time apart from the first commencement.

Tan T - 4 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...