A train can cross a 1200-metre-long bridge completely in 16 seconds. It can cross a 1600-metre-long bridge completely in 20 seconds. What is the speed of the train?

Let's assume the length of train is 'y' metre.

A train can cross a 1200-metre-long bridge completely in 16 seconds.

speed of train = $$\frac{length\ of\ train\ +length\ of\ bridge}{time}$$

= $$\frac{y+1200}{16}$$    Eq.(i)

It can cross a 1600-metre-long bridge completely in 20 seconds.

speed of train = $$\frac{length\ of\ train\ +length\ of\ bridge}{time}$$

= $$\frac{y+1600}{20}$$    Eq.(ii)

So Eq.(i) = Eq.(ii)

$$\frac{y+1200}{16} = \frac{y+1600}{20}$$

$$\frac{y+1200}{4} = \frac{y+1600}{5}$$

5y+6000 = 4y+6400

5y-4y = 6400-6000

y = 400 metre

Put the value of 'y' in Eq.(i).

speed of train = $$\frac{400+1200}{16}$$

= $$\frac{1600}{16}$$

= 100 m/s

We know that 1 km = 1000 m and 1 hour = 3600 seconds.

= $$100\times\frac{3600}{1000}$$ km/h

= 360 km/h