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The speed of the metro train is more than the speed of the bus by 25 km/hr. If the metro starts running from point A to point B while the bus runs from point B to point A and they both meet after 5 hours. Then find the speed of the metro if the distance between A to B is 300 km?
1. 15 km/hr
2. 17.50 km/hr
3. 60 km/hr
4. 42.50 km/hr

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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.

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