A passenger train takes one hour less for a journey of 150 km if its speed is increased by

5 km/hr from the usual speed. Find the usual speed of the train.

Time = distance/speed

Let the speed of the train be ‘a’ km/hr.

Given, passenger train takes one hour less for a journey of 150 km if its speed is increased by

5 km/hr from the usual speed.

⇒ 150(a + 5 – a) = a² + 5a

⇒ a² + 5a – 750 = 0

⇒ a² + 30a – 25a – 750 = 0

⇒ a(a + 30) – 25(a + 30) = 0

⇒ (a – 25)(a + 30) = 0

⇒ a = 25 km/hr