Explanation:

Correct option 3: 14 sec

Train A crosses a man in 8 sec

This means:
Length of Train A = Speed × Time = V × 8

Train A crosses a 180 m platform in 17 sec

So,

Length of Train A+180=V×17

Subtract the two equations:

V×17−V×8=180⇒V(17−8)=180⇒V=180/9=20 m/s

Now plug back to get length of Train A:

L=20×8=160 m

Train A crosses Train B (opp. direction) in 8 sec

Relative speed = 20 (Train A) + 30 (Train B) = 50 m/s
Distance = 50 × 8 = 400 m

So, length of Train B = 400 – 160 = 240 m

Time taken by Train B to cross platform

Length of Train B = 240 m, Platform = 180 m → Total = 420 m
Speed of Train B = 30 m/s

Time=420/30=14 seconds