Puzzle: The Station

@mech-guy-TMwuj2 • Oct 18, 2024

Oct 18, 2024

998

Hi All,

Following is an interesting puzzle i found while browsing,

Every weekday at 6 PM sharp Nawab Gulzarilal arrives by rail at the Lucknow station, and every weekday at the dot of 6 his manservant Ramdayal arrives to drive him home in Lucknow. One day his last appointment cancels and he takes an earlier train, arriving at the station a full hour early. As the day is fair, he elects to take the air and walk home. His manservant picks him up en route, and drives him the rest of the way, arriving 20 minutes earlier than usual.

How long had he been walking?

PS: Except names, Puzzle is copy-pasted from a website.
Mods/Admin: Do i need to quote the source as well?

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mech_guy

@mech-guy-TMwuj2 • Jul 13, 2009

Oh dear!! No takers yet ??
Alright will post the solution in couple of days 😀

Would love to see CEans solve it 😀

Cheers
tech_vaibhav_ee

@tech-vaibhav-ee-65Xzvs • Jul 13, 2009

50 minutes....answer based more on intuision rather than maths...so tell me if i m wrong...
mech_guy

@mech-guy-TMwuj2 • Jul 13, 2009

tech_vaibhav_ee
50 minutes....answer based more on intuision rather than maths...so tell me if i m wrong...
Well your intuition is stronger than your maths i guess 😀

Cheers, yup you are right. He had been walking for 50 minutes.

Anyone with maths/logic rather than intuition ??

Regards
tech_vaibhav_ee

@tech-vaibhav-ee-65Xzvs • Jul 13, 2009

mech_guy
Well your intuition is stronger than your maths i guess 😀

Cheers, yup you are right. He had been walking for 50 minutes.

Anyone with maths/logic rather than intuition ??

Regards
I found out the mathematical solution to it as well:

let us assume the servant leaves the home at y p.m
he reaches the station at = 6:00 pm
time taken to reach station=6-y hrs.
time taken to go back home=6-y hrs.
so reaches the home back at= 6+(6-y)=12-y p.m.

on that special day...
he leaves the home at= y p.m.
suppose they meet midway at some time ,say= x p.m
so time taken by servant to reach his master=x-y hrs
he reaches back at home at= x +(x-y) = 2x - y p.m

now, we know that he reached home 20 min. earlier..
therefore,
2x-y = 12-y -20/60
x=35/6 p.m
therefore , the master walked till x(35/6 p.m.)

since the master started at 5 p.m.
distance walked by the master is= 35/6-5=5/6 hrs = 50 minutes..
mech_guy

@mech-guy-TMwuj2 • Jul 13, 2009

Hi tech_vaibhav,

Solution is cool. Nice work man 😀

Regards