Given:

Ratio of speed of express train to superfast train = 1 ∶ 3

Time taken by superfast train to cross express train completely =  150 seconds

Time taken by passenger in superfast train to cross express train = 60 seconds

Formula used:

Distance = Speed × Time

Relative speed = S_a - S_b       (When both trains are moving in same direction and S_a > S_b)

Calculations:

Let the speed of express train and superfast train be 1x and 3x respectively.

In first case, when superfast train crossed express train completely

Distance covered = Length of express train(l_e)  + Length of superfast train(l_s)

Distance = Speed × Time

⇒ (l_e + l_s) = (3x - 1x) × 150

⇒ (le + ls) = 300x      ----(1)

In second case, when passenger in superfast train crossed express train

Distance covered = Length of express train(le)

Distance = Speed × Time

⇒ (le) = (3x - 1x) × 60

⇒ (le) = 120x      ----(2)

From (1) and (2),

⇒ ls = 180x 

⇒ (le ∶ ls) = 2 ∶ 3

∴ The ratio of the length of an express train to superfast train is 2 ∶ 3.