A train crosses a stationary pole in 20 seconds and a bridge in 32 seconds. If the length of the bridge is 1200 metres, then what is the speed of the train?

Let's assume the length of the train and it's speed are 'y' and 'z' respectively.

A train crosses a stationary pole in 20 seconds.

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

$$z=\frac{y}{20}$$

y = 20z    Eq.(i)

A train crosses a bridge in 32 seconds. If the length of the bridge is 1200 metres.

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

$$z=\frac{y+1200}{32}$$

Put Eq.(i) in the above equation.

$$z=\frac{20z+1200}{32}$$

32z = 20z+1200

32z-20z = 1200

12z = 1200

z = 100

Speed of the train = 100 m/s

= $$100\times\frac{3600}{1000}$$ km/h [1km = 1000m and 1 hour = 3600 seconds]

= 360 km/h