A Train which travels at the uniform rate of 30 m/s leaves Pune for Mumbai at 10 a.m. At what distance from Pune will it meet a train which…

Speed of train leaving Pune = 30m/s = 30 × (18/5) = 108 km/h

Speed of train leaving Mumbai = 30 × (2/3) = 20 m/s = 20 × (18/5) = 72 km/h

Let the time at which they meet be “t” hours from the start.

We know that,

Distance = Speed × Time

For the train leaving Pune, Distance covered in “t” hours = 108t km

For the train leaving Mumbai, Distance covered in “t” hours = 72t km

Clearly, as total distance = 90 km

⇒ 108t + 72t = 90

⇒ 180t = 90

⇒ t = 0.5 hours.

Distance covered by train leaving from Pune in 0.5 hours = 108t =108 × 0.5 = 54 km

∴ The trains meet at a distance of 54 km from Pune.