A train can cover a certain distance in 3 hrs. If the track management is improved, an increase in the speed of the train by 10 km/h is possible, which can reduce the above journey time by 30 minutes. Find the initial speed of the train.

Let's assume the distance is 'd' and the initial speed of the train is 's'.

A train can cover a certain distance in 3 hrs.

distance = initial speed of the train $$\times$$ time

d = s $$\times$$ 3

d = 3s    Eq.(i)

If the track management is improved, an increase in the speed of the train by 10 km/h is possible, which can reduce the above journey time by 30 minutes.

1 hour = 60 minutes

0.5 hour = 30 minutes

distance = speed of the train after track management is improved $$\times$$ time

d = (s+10) $$\times$$ (3-0.5)

d = (s+10) $$\times$$ 2.5

d = 2.5(s+10)    Eq.(ii)

So Eq.(i) = Eq.(ii).

3s = 2.5(s+10)

30s = 25(s+10)

6s = 5(s+10)

6s = 5s+50

s = 50 km/h

the initial speed of the train = 50 km/h