Correct Answer - Option 4 : 42.50 km/hr
Given:
The speed of metro train is more than the speed of bus by 25 km/hr.
Metro train started running from point A to point B while bus runs from point B to point A.
Distance covered = 300 km
Time = 5 hours
Concepts used:
Relative speed in opposite direction = Speed of metro train + speed of bus
Time = Distance/Relative speed
Calculation:
Let the speed of the bus be x km/hr.
The speed of the metro train is more than the speed of the bus by 25 km/hr.
So, Speed of metro = x + 25 km/hr
Relative speed in opposite direction = Speed of metro train + speed of bus
⇒ x + x + 25 = 2x + 25 km/hr
Distance covered = 300 km
Time = 5 hours
Time = Distance/Relative speed
⇒ 5 = 300/(2x + 25)
⇒ 5 × (2x + 25) = 300
⇒ 10x + 125 = 300
⇒ 10x = 300 – 125
⇒ x = 175/10 km/hr
⇒ x = 17.50 km/hr
Speed of bus = x = 17.50 km/hr
Speed of metro train = x + 25 km/hr
⇒ 17.50 km/hr + 25 km/hr
⇒ 42.50 km/hr
∴ Speed of metro train is 42.50 km/hr.