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.
\(\Rightarrow \frac{150}{a}-\frac{150}{a+5}=1\)
⇒ 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