A bus takes 2 hrs less for a journey of 300 km, if its speed is increased by 5km/hr from its usual speed, then the usual speed in km/hr is

Solution : -

Let the usual speed of bus be x km/hr.

Time = Distance / Speed = 300/x hrs

According to the question,

=> (300/x - 2) (x + 5) = 300

=> (300 - 2x) / x (x + 5) = 300

=> 300x + 1500 - 2x² - 10x = 300x

=> 2x² + 10x - 1500 = 0

=> 2 (x² + 5x - 750) = 0

=> x² + 30x - 25x - 750 = 0

=> x (x + 30) - 25 (x + 30) = 0

=> (x - 25) (x + 30) = 0

=> x = 25 or x = - 30

∴ x ≠ - 30 (Because speed can't be negative)

Hence,

The usual speed of bus = 25 km/hr