Correct Answer - Option 3 : 9 : 4

**Given:**

Length of train = 180 m

Speed of the train = 54 km/hr

Train crosses a platform in 20 seconds and crosses a tunnel in 30 seconds.

**Formula Used:**

Distance = Speed × Time

**Calculation:**

Suppose the length of the platform and the tunnel is x m and y m, respectively.

Speed of the train = 54 × 5/18 = 15 m/s

**Case I:** Train crosses the platform in 20 seconds

⇒ (180 + x) = 15 × 20

⇒ 180 + x = 300

⇒ x = 120 m

The length of the platform is 120 m.

**Case II:** Train crosses the tunnel in 30 seconds.

⇒ (180 + y) = 15 × 30

⇒ 180 + y = 450

⇒ y = 450 – 180

⇒ y = 270 m

the ratio between the length of tunnel and the length of the platform is 270 : 120 = 9 : 4

**∴ Required ratio is 9 : 4**