The length of train X is 80\% more than that of train Y. The speed of train X is $108 ext{ km/h}$, and it crosses a bridge in $20$ seconds. The ratio of the speeds of train X to train Y is $5:3$. Find the time taken by train Y to cross a distance of $200$ meters (in seconds).

Question

The length of train X is 80\% more than that of train Y. The speed of train X is $108 	ext{ km/h}$, and it crosses a bridge in $20$ seconds. The ratio of the speeds of train X to train Y is $5:3$. Find the time taken by train Y to cross a distance of $200$ meters (in seconds).

Accepted Answer

**Solution:**

1. Let the length of train Y be $L$ meters. Then the length of train X is $L + 0.8L = 1.8L$ meters.

2. Speed of train X is given as $108 	ext{ km/h}$. Convert this to meters per second:
   $$108 	imes \frac{1000}{3600} = 30 	ext{ m/s}$$

3. Train X crosses a bridge in $20$ seconds. The distance covered in this time is the length of the train plus the length of the bridge.

Let the length of the bridge be $B$ meters.

Distance covered by train X while crossing the bridge:
   $$1.8L + B = 30 	imes 20 = 600 	ext{ meters}$$

4. The ratio of speeds of train X to train Y is $5:3$. Since train X speed is $30 	ext{ m/s}$, train Y speed is:
   $$\frac{3}{5} 	imes 30 = 18 	ext{ m/s}$$

5. We want to find the time taken by train Y to cross $200$ meters. The time depends on the length of train Y plus $200$ meters (if the train is crossing a platform or a bridge of length $200$ meters), or just $200$ meters if the train length is not involved.

However, the problem does not specify whether the $200$ meters is a bridge, platform, or just a distance to be crossed by the train's front.

6. Also, the length $L$ of train Y is unknown, and the length of the bridge $B$ is unknown.

7. From the given data, we cannot find $L$ or $B$ individually because we have only one equation:
   $$1.8L + B = 600$$

Without knowing either $L$ or $B$, we cannot determine the exact time for train Y to cross $200$ meters.

**Answer:** Can’t be determined

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