Two trains start from the same point simultaneously and in the same direction. The first train travels at 40 km /h, and the speed of the second train is 25% more than the speed of first train. Thirty minutes later, a third train starts from same point and in the same direction. It over takes the second train 90 minutes later than it overtook the first train. What is the speed of the third train?

Solution(By Examveda Team)

A _______ B ________ C
Let both the trains start from point A.
At point B third train overtook the first train.
To overtake the first train by third train, Third train needs to cover,
Distance covered by first train in $$1\frac{1}{2}$$ h = distance covered by third train in 1 h.
[as third train has started 30 minutes later]
In this situation distance is constant,
then from,
s × t = d; we get, S α $$\frac{1}{{\text{t}}}$$
Now,
$$\eqalign{ & \frac{{{\text{t}} + \frac{1}{2}}}{{\text{t}}} = \frac{{\text{s}}}{{40}} \cr & \frac{{2{\text{t}} + 1}}{{\text{t}}} = \frac{{\text{s}}}{{40}}\,.\,.\,.\,.\,.\,.\,.\,.\left( 1 \right) \cr} $$
From equation (1),
It is clear that time is in the ratio 3 : 2 then speed will be in 2 : 3 ratios.
Hence, Speed of the Third train will be 60 km/h.