A train travels between X and Y in 3 hours. When the speed of train is increased by 6 km/hr, then it covers the same distance in 2 hours. What is the original speed of train?

Question: A train travels between X and Y in 3 hours. When the speed of train is increased by 6 km/hr, then it covers the same distance in 2 hours. What is the original speed of train?

Solution:
Let the original speed of the train be a km/hr.
The distance between X and Y is the same in both cases.

Now, given that,
Speed = a km/hr
Time = 3 hours
∴ Distance = a × 3 = 3a km

And,
Speed = (a + 6) km/hr
Time = 2 hours
∴ Distance = (a + 6) × 2 = 2(a + 6) km

Since distance is the same. Then we get,
⇒ 3a = 2(a + 6)
⇒ 3a = 2a + 12
⇒ 3a - 2a = 12
∴ a = 12

So the original speed of the train is 12 km/hr