Convert Train Speed

The train's speed is given in km/h and needs to be converted to m/s for calculations involving seconds.

Speed $= 36 \text{ km/h}$
Speed $= 36 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 36 \times \frac{5}{18} \text{ m/s}$
Speed $= 10 \text{ m/s}$

Calculate Train Length

When the train crosses a mark, it covers a distance equal to its own length.

Length of Train ($L_t$) = Speed $\times$ Time to cross mark
$L_t = 10 \text{ m/s} \times 8 \text{ sec}$
$L_t = 80 \text{ m}$

Calculate Total Distance Covered

When the train crosses the platform, the total distance covered is the sum of the train's length and the platform's length.

Total Distance ($L_{total}$) = Speed $\times$ Time to cross platform
$L_{total} = 10 \text{ m/s} \times 20 \text{ sec}$
$L_{total} = 200 \text{ m}$

Determine Platform Length

The length of the platform is the difference between the total distance covered and the length of the train.

Length of Platform ($L_p$) = Total Distance - Length of Train
$L_p = L_{total} - L_t$
$L_p = 200 \text{ m} - 80 \text{ m}$
$L_p = 120 \text{ m}$

The length of the platform is 120 m.