A train P going at the speed of 58 km/hr completely passes train Q of length 238 m, going in the same direction on parallel tracks, at 27 km/hr, in 7.5 minutes. How much time (in seconds) will P take to cross completely train R of length 123 m, going at 38 km/hr in the opposite direction?​

Correct option is C

Given:

Train P speed = 58 km/hr

Train Q speed = 27 km/hr

Length of Train Q = 238 m

Time taken to overtake Train Q = 7.5 minutes = 450 seconds

Train R speed = 38 km/hr

Length of Train R = 123 m

Formula Used:

Relative speed (same direction) = Difference of speeds

Relative speed (opposite direction) = Sum of speeds

Speed conversion: 1 km/hr = $$\frac{5}{18} \text{ m/s}$$​​

Time = Distance ÷ Speed

Solution:

Relative speed of P and Q = 58 - 27 = 31 km/hr = $$\frac{155}{18} \text{ m/s}$$​​

Distance = $$\frac{155}{18} \times 450 = 3875 \text{ m}$$​​

Let the length of Train P = L

L + 238 = 3875

L = 3875 - 238 = 3637 m

Now, 

Relative speed of P and R =58 + 38 = 96 km/hr = $$\frac{80}{3} \text{ m/s}$$​​

Total distance to be covered = 3637 + 123 = 3760 m

Time = $$\frac{3760}{80/3} = 3760 \times \frac{3}{80} = \frac{11280}{80} = 141 \text{ seconds}$$​​

Thus, Train P will take 141 seconds to completely cross Train R