The length of train A is $300$ meters and it crosses a $500$ meters long platform in $30$ seconds. If the length of train B is twice the length of train A and the speed of train B is $198 ext{ km/hr}$, then find the time taken by train B to cross the same platform (in seconds).

Question

The length of train A is $300$ meters and it crosses a $500$ meters long platform in $30$ seconds. If the length of train B is twice the length of train A and the speed of train B is $198 	ext{ km/hr}$, then find the time taken by train B to cross the same platform (in seconds).

Accepted Answer

**Solution:**

1. First, calculate the speed of train A.
   - Length of train A = $300$ meters
   - Length of platform = $500$ meters
   - Total distance covered by train A while crossing the platform = $300 + 500 = 800$ meters
   - Time taken by train A = $30$ seconds

2. Speed of train A in meters per second:
   $$	ext{Speed} = \frac{	ext{Distance}}{	ext{Time}} = \frac{800}{30} = \frac{80}{3} 	ext{ m/s}$$

3. Length of train B = $2 	imes 300 = 600$ meters

4. Speed of train B is given as $198 	ext{ km/hr}$. Convert it to meters per second:
   $$198 	imes \frac{5}{18} = 55 	ext{ m/s}$$

5. Total distance train B needs to cover to cross the platform:
   $$600 + 500 = 1100 	ext{ meters}$$

6. Time taken by train B to cross the platform:
   $$	ext{Time} = \frac{	ext{Distance}}{	ext{Speed}} = \frac{1100}{55} = 20 	ext{ seconds}$$

**Answer:** $20$ seconds

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