A train Pawan express of length 380 m running with the speed of 108 km/h crosses a platform of certain length in 37 seconds. Another train, Toofan express of certain length running with a speed of 90 km/h crosses the platform in 42.6 seconds. What will be the time taken by both trains to cross each other if they run in opposite directions?

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**Solution:**

1. Convert speeds from km/h to m/s:
   - Speed of Pawan express = $\frac{5}{18} 	imes 108 = 30 	ext{ m/s}$
   - Speed of Toofan express = $\frac{5}{18} 	imes 90 = 25 	ext{ m/s}$

2. Let the length of the platform be $x$ meters and length of Toofan express be $y$ meters.

3. Using the time taken by Pawan express to cross the platform:
   $$\frac{380 + x}{30} = 37$$
   $$380 + x = 37 	imes 30 = 1110$$
   $$x = 1110 - 380 = 730 	ext{ m}$$

4. Using the time taken by Toofan express to cross the platform:
   $$\frac{y + 730}{25} = 42.6$$
   $$y + 730 = 42.6 	imes 25 = 1065$$
   $$y = 1065 - 730 = 335 	ext{ m}$$

5. When both trains run in opposite directions, their relative speed is:
   $$30 + 25 = 55 	ext{ m/s}$$

6. Total length to be crossed when trains cross each other:
   $$380 + 335 = 715 	ext{ m}$$

7. Time taken to cross each other:
   $$\frac{715}{55} = 13 	ext{ seconds}$$

**Answer:** 13 seconds

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