# A train crosses a platform and a tunnel in 20 seconds and 30 seconds, respectively. The speed of the train and length of the train are 54 km/hr and 18

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A train crosses a platform and a tunnel in 20 seconds and 30 seconds, respectively. The speed of the train and length of the train are 54 km/hr and 180 metres, respectively. Find the ratio between the length of the tunnel and the length of platform?

1. 3 : 8
2. 4 : 5
3. 9 : 4
4. 9 : 5
5. 3 : 4

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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