a different concept needs more innovative solution

[ashish1354]

i am finding it very difficult to solve this by counting all the hour intervals
even if i do reconciling the intervals is very difficult. can someone one help??

[4meonly]

Somebody has any idea with this stuff?
It seemes to me that (15 p.m. + 10x) and (16+15y) will have someday one LCM - the same time...
Every 2 numbers always have LCM. Than we should divide LCM by 7 and add ther remainder to Monday...
if I am not missing something

But what is the LCM?

[pseudononymous]

B: 10, 20, 30, 40, etc
C: 16, 31, 46, 51, etc.

They'll never leave at the same time.

[lunarpower]

yeah, just find the least common multiple. once the LCM number of hours has passed, the buses will be separated by exactly the same time interval as before - which means that an entire "cycle" of behavior has occurred. in other words, the buses' behavior is periodic, with a complete period equal to the LCM of the times.

since one of the buses leaves every ten hours and the other one leaves every fifteen hours, the LCM is only thirty hours.
this means that you only have to look at the first 30 hours. if there are no coincident departures in the first 30 hours, then there will never be any coincident departures.

if you look at the first thirty hours, then the buses will never leave at the same time. therefore, (e) is the answer.

--

by the way, pure pattern recognition (see the post by "pseudononymous") is a perfectly viable and honorable way to solve this problem. a quick glimpse at the units digits reveals, in short order, that the departures will never occur at the same time.