Question

if niti drives her car at to km/hr from her home,she reaches the office late by 10min.however if she drives at 60km/hr,she reaches the office 5 minutes early .find the distance of the office from her home.

Answer 1

Hi,

Let d be the distance
let t be the time taken (without being early or late)

the hint here is that the distance remains same in both cases
so the distances in given two cases can be equated to each other

speed = distance / time
distance = speed * time

50*(t+10/60) = 60*(t-5/60)
=> 50t + 500/60 = 60t - 5
=> 10t = 500/60 + 5
=> 10t = 800/60
=> t = 80/60 = 4/3 hrs

note: 10 minutes = 10/60 hrs & similarly 5 minutes = 5/60 hrs

so distance
= 60*(t-5/60)
= 60t - 5
= 60*(4/3) - 5
= 240/3 - 5
= 80 - 5
= 75 km

So the distance of the office from home is 75 km

Hope it helped.
Let me know if any doubts.
Cheers !!!